[ { "text": "Quantitative field theory of the glass transition: We develop a full microscopic replica field theory of the dynamical\ntransition in glasses. By studying the soft modes that appear at the dynamical\ntemperature we obtain an effective theory for the critical fluctuations. This\nanalysis leads to several results: we give expressions for the mean field\ncritical exponents, and we study analytically the critical behavior of a set of\nfour-points correlation functions from which we can extract the dynamical\ncorrelation length. Finally, we can obtain a Ginzburg criterion that states the\nrange of validity of our analysis. We compute all these quantities within the\nHypernetted Chain Approximation (HNC) for the Gibbs free energy and we find\nresults that are consistent with numerical simulations.", "category": "cond-mat_dis-nn" }, { "text": "Critical indices of Anderson transition: something is wrong with\n numerical results: Numerical results for Anderson transition are critically discussed. A simple\nprocedure to deal with corrections to scaling is suggested. With real\nuncertainties taken into account, the raw data are in agreement with a value\n$\\nu=1$ for the critical index of the correlation length in three dimensions.", "category": "cond-mat_dis-nn" }, { "text": "A Generalized Rate Model for Neuronal Ensembles: There has been a long-standing controversy whether information in neuronal\nnetworks is carried by the firing rate code or by the firing temporal code. The\ncurrent status of the rivalry between the two codes is briefly reviewed with\nthe recent studies such as the brain-machine interface (BMI). Then we have\nproposed a generalized rate model based on the {\\it finite} $N$-unit Langevin\nmodel subjected to additive and/or multiplicative noises, in order to\nunderstand the firing property of a cluster containing $N$ neurons. The\nstationary property of the rate model has been studied with the use of the\nFokker-Planck equation (FPE) method. Our rate model is shown to yield various\nkinds of stationary distributions such as the interspike-interval distribution\nexpressed by non-Gaussians including gamma, inverse-Gaussian-like and\nlog-normal-like distributions.\n The dynamical property of the generalized rate model has been studied with\nthe use of the augmented moment method (AMM) which was developed by the author\n[H. Hasegawa, J. Phys. Soc. Jpn. 75 (2006) 033001]. From the macroscopic point\nof view in the AMM, the property of the $N$-unit neuron cluster is expressed in\nterms of {\\it three} quantities; $\\mu$, the mean of spiking rates of $R=(1/N)\n\\sum_i r_i$ where $r_i$ denotes the firing rate of a neuron $i$ in the cluster:\n$\\gamma$, averaged fluctuations in local variables ($r_i$): $\\rho$,\nfluctuations in global variable ($R$). We get equations of motions of the three\nquantities, which show $\\rho \\sim \\gamma/N$ for weak couplings. This implies\nthat the population rate code is generally more reliable than the single-neuron\nrate code. Our rate model is extended and applied to an ensemble containing\nmultiple neuron clusters.", "category": "cond-mat_dis-nn" }, { "text": "Statistical Properties of Ideal Ensemble of Disordered 1D Steric\n Spin-Chains: The statistical properties of ensemble of disordered 1D steric spin-chains\n(SSC) of various length are investigated. Using 1D spin-glass type classical\nHamiltonian, the recurrent trigonometrical equations for stationary points and\ncorresponding conditions for the construction of stable 1D SSCs are found. The\nideal ensemble of spin-chains is analyzed and the latent interconnections\nbetween random angles and interaction constants for each set of three\nnearest-neighboring spins are found. It is analytically proved and by numerical\ncalculation is shown that the interaction constant satisfies L\\'{e}vy's\nalpha-stable distribution law. Energy distribution in ensemble is calculated\ndepending on different conditions of possible polarization of spin-chains. It\nis specifically shown that the dimensional effects in the form of set of local\nmaximums in the energy distribution arise when the number of spin-chains M <<\nN_x^2 (where N_x is number of spins in a chain) while in the case when M ~\nN_x^2 energy distribution has one global maximum and ensemble of spin-chains\nsatisfies Birkhoff's ergodic theorem. Effective algorithm for parallel\nsimulation of problem which includes calculation of different statistic\nparameters of 1D SSCs ensemble is elaborated.", "category": "cond-mat_dis-nn" }, { "text": "Mean field treatment of exclusion processes with random-force disorder: The asymmetric simple exclusion process with random-force disorder is studied\nwithin the mean field approximation. The stationary current through a domain\nwith reversed bias is analyzed and the results are found to be in accordance\nwith earlier intuitive assumptions. On the grounds of these results, a\nphenomenological random barrier model is applied in order to describe\nquantitatively the coarsening phenomena. Predictions of the theory are compared\nwith numerical results obtained by integrating the mean field evolution\nequations.", "category": "cond-mat_dis-nn" }, { "text": "Statistical Properties of the one dimensional Anderson model relevant\n for the Nonlinear Schr\u00f6dinger Equation in a random potential: The statistical properties of overlap sums of groups of four eigenfunctions\nof the Anderson model for localization as well as combinations of four\neigenenergies are computed. Some of the distributions are found to be scaling\nfunctions, as expected from the scaling theory for localization. These enable\nto compute the distributions in regimes that are otherwise beyond the\ncomputational resources. These distributions are of great importance for the\nexploration of the Nonlinear Schr\\\"odinger Equation (NLSE) in a random\npotential since in some explorations the terms we study are considered as noise\nand the present work describes its statistical properties.", "category": "cond-mat_dis-nn" }, { "text": "Antiferromagnetic effects in Chaotic Map lattices with a conservation\n law: Some results about phase separation in coupled map lattices satisfying a\nconservation law are presented. It is shown that this constraint is the origin\nof interesting antiferromagnetic effective couplings and allows transitions to\nantiferromagnetic and superantiferromagnetic phases. Similarities and\ndifferences between this models and statistical spin models are pointed out.", "category": "cond-mat_dis-nn" }, { "text": "Disordered and ordered states of exactly solvable Ising-Heisenberg\n planar models with a spatial anisotropy: Ground-state and finite-temperature properties of a special class of exactly\nsolvable Ising-Heisenberg planar models are examined using the generalized\ndecoration-iteration and star-triangle mapping transformations. The\ninvestigated spin systems exhibit an interesting quantum behaviour manifested\nin a remarkable geometric spin frustration, which appears notwithstanding the\npurely ferromagnetic interactions of the considered model systems. This kind of\nspin frustration originates from an easy-plane anisotropy in the XXZ Heisenberg\ninteraction between nearest-neighbouring spins that favours ferromagnetic\nordering of their transverse components, whereas their longitudinal components\nare aligned antiferomagnetically.", "category": "cond-mat_dis-nn" }, { "text": "Geometrical organization of solutions to random linear Boolean equations: The random XORSAT problem deals with large random linear systems of Boolean\nvariables. The difficulty of such problems is controlled by the ratio of number\nof equations to number of variables. It is known that in some range of values\nof this parameter, the space of solutions breaks into many disconnected\nclusters. Here we study precisely the corresponding geometrical organization.\nIn particular, the distribution of distances between these clusters is computed\nby the cavity method. This allows to study the `x-satisfiability' threshold,\nthe critical density of equations where there exist two solutions at a given\ndistance.", "category": "cond-mat_dis-nn" }, { "text": "Random sequential adsorption of shrinking or spreading particles: We present a model of one-dimensional irreversible adsorption in which\nparticles once adsorbed immediately shrink to a smaller size or expand to a\nlarger size. Exact solutions for the fill factor and the particle number\nvariance as a function of the size change are obtained. Results are compared\nwith approximate analytical solutions.", "category": "cond-mat_dis-nn" }, { "text": "Anomalous Roughening in Experiments of Interfaces in Hele-Shaw Flows\n with Strong Quenched Disorder: We report experimental evidences of anomalous kinetic roughening in the\nstable displacement of an oil-air interface in a Hele-Shaw cell with strong\nquenched disorder. The disorder consists on a random modulation of the gap\nspacing transverse to the growth direction (tracks). We have performed\nexperiments varying average interface velocity and gap spacing, and measured\nthe scaling exponents. We have obtained beta=0.50, beta*=0.25, alpha=1.0,\nalpha_l=0.5, and z=2. When there is no fluid injection, the interface is driven\nsolely by capillary forces, and a higher value of beta around beta=0.65 is\nmeasured. The presence of multiscaling and the particular morphology of the\ninterfaces, characterized by high slopes that follow a L\\'evy distribution,\nconfirms the existence of anomalous scaling. From a detailed study of the\nmotion of the oil--air interface we show that the anomaly is a consequence of\ndifferent local velocities over tracks plus the coupling in the motion between\nneighboring tracks. The anomaly disappears at high interface velocities, weak\ncapillary forces, or when the disorder is not sufficiently persistent in the\ngrowth direction. We have also observed the absence of scaling when the\ndisorder is very strong or when a regular modulation of the gap spacing is\nintroduced.", "category": "cond-mat_dis-nn" }, { "text": "On the mechanical beta relaxation in glass and its relation to the\n double-peak phenomenon in impulse excited vibration at high temperatures: A viscoelastic model is established to reveal the relation between alpha-beta\nrelaxation of glass and the double-peak phenomenon in the experiments of\nimpulse excited vibration. In the modelling, the normal mode analysis (NMA) of\npotential energy landscape (PEL) picture is employed to describe mechanical\nalpha and beta relaxations in a glassy material. The model indicates that a\nsmall beta relaxation can lead to an apparent double-peak phenomenon resulted\nfrom the free vibration of a glass beam when the frequency of beta relaxation\npeak is close to the natural frequency of specimen. The theoretical prediction\nis validated by the acoustic spectrum of a fluorosilicate glass beam excited by\na mid-span impulse. Furthermore, the experimental results indicate a negative\ntemperature-dependence of the frequency of beta relaxation in the\nfluorosilicate glass S-FSL5 which can be explained based on the physical\npicture of fragmented oxide-network patches in liquid-like regions.", "category": "cond-mat_dis-nn" }, { "text": "Dependence of critical parameters of 2D Ising model on lattice size: For the 2D Ising model, we analyzed dependences of thermodynamic\ncharacteristics on number of spins by means of computer simulations. We\ncompared experimental data obtained using the Fisher-Kasteleyn algorithm on a\nsquare lattice with $N=l{\\times}l$ spins and the asymptotic Onsager solution\n($N\\to\\infty$). We derived empirical expressions for critical parameters as\nfunctions of $N$ and generalized the Onsager solution on the case of a\nfinite-size lattice. Our analytical expressions for the free energy and its\nderivatives (the internal energy, the energy dispersion and the heat capacity)\ndescribe accurately the results of computer simulations. We showed that when\n$N$ increased the heat capacity in the critical point increased as $lnN$. We\nspecified restrictions on the accuracy of the critical temperature due to\nfinite size of our system. Also in the finite-dimensional case, we obtained\nexpressions describing temperature dependences of the magnetization and the\ncorrelation length. They are in a good qualitative agreement with the results\nof computer simulations by means of the dynamic Metropolis Monte Carlo method.", "category": "cond-mat_dis-nn" }, { "text": "k-Core percolation on multiplex networks: We generalize the theory of k-core percolation on complex networks to k-core\npercolation on multiplex networks, where k=(k_a, k_b, ...). Multiplex networks\ncan be defined as networks with a set of vertices but different types of edges,\na, b, ..., representing different types of interactions. For such networks, the\nk-core is defined as the largest sub-graph in which each vertex has at least\nk_i edges of each type, i = a, b, ... . We derive self-consistency equations to\nobtain the birth points of the k-cores and their relative sizes for\nuncorrelated multiplex networks with an arbitrary degree distribution. To\nclarify our general results, we consider in detail multiplex networks with\nedges of two types, a and b, and solve the equations in the particular case of\nER and scale-free multiplex networks. We find hybrid phase transitions at the\nemergence points of k-cores except the (1,1)-core for which the transition is\ncontinuous. We apply the k-core decomposition algorithm to air-transportation\nmultiplex networks, composed of two layers, and obtain the size of (k_a,\nk_b)-cores.", "category": "cond-mat_dis-nn" }, { "text": "The replica symmetric region in the Sherrington-Kirkpatrick mean field\n spin glass model. The Almeida-Thouless line: In previous work, we have developed a simple method to study the behavior of\nthe Sherrington-Kirkpatrick mean field spin glass model for high temperatures,\nor equivalently for high external fields. The basic idea was to couple two\ndifferent replicas with a quadratic term, trying to push out the two replica\noverlap from its replica symmetric value. In the case of zero external field,\nour results reproduced the well known validity of the annealed approximation,\nup to the known critical value for the temperature. In the case of nontrivial\nexternal field, our method could prove the validity of the\nSherrington-Kirkpatrick replica symmetric solution up to a line, which fell\nshort of the Almeida-Thouless line, associated to the onset of the spontaneous\nreplica symmetry breaking, in the Parisi Ansatz. Here, we make a strategic\nimprovement of the method, by modifying the flow equations, with respect to the\nparameters of the model. We exploit also previous results on the overlap\nfluctuations in the replica symmetric region. As a result, we give a simple\nproof that replica symmetry holds up to the critical Almeida-Thouless line, as\nexpected on physical grounds. Our results are compared with the\ncharacterization of the replica symmetry breaking line previously given by\nTalagrand. We outline also a possible extension of our methods to the broken\nreplica symmetry region.", "category": "cond-mat_dis-nn" }, { "text": "Liquid markets and market liquids: collective and single-asset dynamics\n in financial markets: We characterize the collective phenomena of a liquid market. By interpreting\nthe behavior of a no-arbitrage N asset market in terms of a particle system\nscenario, (thermo)dynamical-like properties can be extracted from the asset\nkinetics. In this scheme the mechanisms of the particle interaction can be\nwidely investigated. We test the verisimilitude of our construction on\ntwo-decade stock market daily data (DAX30) and show the result obtained for the\ninteraction potential among asset pairs.", "category": "cond-mat_dis-nn" }, { "text": "A Mean-field Approach for an Intercarrier Interference Canceller for\n OFDM: The similarity of the mathematical description of random-field spin systems\nto orthogonal frequency-division multiplexing (OFDM) scheme for wireless\ncommunication is exploited in an intercarrier-interference (ICI) canceller used\nin the demodulation of OFDM. The translational symmetry in the Fourier domain\ngenerically concentrates the major contribution of ICI from each subcarrier in\nthe subcarrier's neighborhood. This observation in conjunction with mean field\napproach leads to a development of an ICI canceller whose necessary cost of\ncomputation scales linearly with respect to the number of subcarriers. It is\nalso shown that the dynamics of the mean-field canceller are well captured by a\ndiscrete map of a single macroscopic variable, without taking the spatial and\ntime correlations of estimated variables into account.", "category": "cond-mat_dis-nn" }, { "text": "Statistical Design of Chaotic Waveforms with Enhanced Targeting\n Capabilities: We develop a statistical theory of waveform shaping of incident waves that\naim to efficiently deliver energy at weakly lossy targets which are embedded\ninside chaotic enclosures. Our approach utilizes the universal features of\nchaotic scattering -- thus minimizing the use of information related to the\nexact characteristics of the chaotic enclosure. The proposed theory applies\nequally well to systems with and without time-reversal symmetry.", "category": "cond-mat_dis-nn" }, { "text": "Critical behavior of a cellular automaton highway traffic model: We derive the critical behavior of a CA traffic flow model using an order\nparameter breaking the symmetry of the jam-free phase. Random braking appears\nto be the symmetry-breaking field conjugate to the order parameter. For\n$v_{\\max}=2$, we determine the values of the critical exponents $\\beta$,\n$\\gamma$ and $\\delta$ using an order-3 cluster approximation and computer\nsimulations. These critical exponents satisfy a scaling relation, which can be\nderived assuming that the order parameter is a generalized homogeneous function\nof $|\\rho-\\rho_c|$ and p in the vicinity of the phase transition point.", "category": "cond-mat_dis-nn" }, { "text": "Entropy of complex relevant components of Boolean networks: Boolean network models of strongly connected modules are capable of capturing\nthe high regulatory complexity of many biological gene regulatory circuits. We\nstudy numerically the previously introduced basin entropy, a parameter for the\ndynamical uncertainty or information storage capacity of a network as well as\nthe average transient time in random relevant components as a function of their\nconnectivity. We also demonstrate that basin entropy can be estimated from\ntime-series data and is therefore also applicable to non-deterministic networks\nmodels.", "category": "cond-mat_dis-nn" }, { "text": "The metastable minima of the Heisenberg spin glass in a random magnetic\n field: We have studied zero temperature metastable states in classical $m$-vector\ncomponent spin glasses in the presence of $m$-component random fields (of\nstrength $h_{r}$) for a variety of models, including the Sherrington\nKirkpatrick (SK) model, the Viana Bray (VB) model and the randomly diluted\none-dimensional models with long-range power law interactions. For the SK model\nwe have calculated analytically its complexity (the log of the number of\nminima) for both the annealed case and the quenched case, both for fields above\nand below the de Almeida Thouless (AT) field ($h_{AT} > 0$ for $m>2$). We have\ndone quenches starting from a random initial state by putting spins parallel to\ntheir local fields until convergence and found that in zero field it always\nproduces minima which have zero overlap with each other. For the $m=2$ and\n$m=3$ cases in the SK model the final energy reached in the quench is very\nclose to the energy $E_c$ at which the overlap of the states would acquire\nreplica symmetry breaking features. These minima have marginal stability and\nwill have long-range correlations between them. In the SK limit we have\nanalytically studied the density of states $\\rho(\\lambda)$ of the Hessian\nmatrix in the annealed approximation. Despite the absence of continuous\nsymmetries, the spectrum extends down to zero with the usual $\\sqrt{\\lambda}$\nform for the density of states for $h_{r}h_{AT}$, there is a gap in the spectrum which closes up as $h_{AT}$ is\napproached. For the VB model and the other models our numerical work shows that\nthere always exist some low-lying eigenvalues and there never seems to be a\ngap. There is no sign of the AT transition in the quenched states reached from\ninfinite temperature for any model but the SK model, which is the only model\nwhich has zero complexity above $h_{AT}$.", "category": "cond-mat_dis-nn" }, { "text": "A theoretical model of neuronal population coding of stimuli with both\n continuous and discrete dimensions: In a recent study the initial rise of the mutual information between the\nfiring rates of N neurons and a set of p discrete stimuli has been analytically\nevaluated, under the assumption that neurons fire independently of one another\nto each stimulus and that each conditional distribution of firing rates is\ngaussian. Yet real stimuli or behavioural correlates are high-dimensional, with\nboth discrete and continuously varying features.Moreover, the gaussian\napproximation implies negative firing rates, which is biologically implausible.\nHere, we generalize the analysis to the case where the stimulus or behavioural\ncorrelate has both a discrete and a continuous dimension. In the case of large\nnoise we evaluate the mutual information up to the quadratic approximation as a\nfunction of population size. Then we consider a more realistic distribution of\nfiring rates, truncated at zero, and we prove that the resulting correction,\nwith respect to the gaussian firing rates, can be expressed simply as a\nrenormalization of the noise parameter. Finally, we demonstrate the effect of\naveraging the distribution across the discrete dimension, evaluating the mutual\ninformation only with respect to the continuously varying correlate.", "category": "cond-mat_dis-nn" }, { "text": "Cascading Parity-Check Error-Correcting Codes: A method for improving the performance of sparse-matrix based parity check\ncodes is proposed, based on insight gained from methods of statistical physics.\nThe advantages of the new approach are demonstrated on an existing\nencoding/decoding paradigm suggested by Sourlas. We also discuss the\napplication of the same method to more advanced codes of a similar type.", "category": "cond-mat_dis-nn" }, { "text": "Absorbing phase transitions in a non-conserving sandpile model: We introduce and study a non-conserving sandpile model, the autonomously\nadapting sandpile (AAS) model, for which a site topples whenever it has two or\nmore grains, distributing three or two grains randomly on its neighboring\nsites, respectively with probability $p$ and $(1-p)$. The toppling process is\nindependent of the actual number of grains $z_i$ of the toppling site, as long\nas $z_i\\ge2$. For a periodic lattice the model evolves into an inactive state\nfor small $p$, with the number of active sites becoming stationary for larger\nvalues of $p$. In one and two dimensions we find that the absorbing phase\ntransition occurs for $p_c\\!\\approx\\!0.717$ and $p_c\\!\\approx\\!0.275$.\n The symmetry of bipartite lattices allows states in which all active sites\nare located alternatingly on one of the two sublattices, A and B, respectively\nfor even and odd times. We show that the AB-sublattice symmetry is\nspontaneously broken for the AAS model, an observation that holds also for the\nManna model. One finds that a metastable AB-symmetry conserving state is\ntransiently observable and that it has the potential to influence the width of\nthe scaling regime, in particular in two dimensions.\n The AAS model mimics the behavior of integrate-and-fire neurons which\npropagate activity independently of the input received, as long as the\nthreshold is crossed. Abstracting from regular lattices, one can identify sites\nwith neurons and consider quenched networks of neurons connected to a fixed\nnumber $G$ of other neurons, with $G$ being drawn from a suitable distribution.\nThe neuronal activity is then propagated to $G$ other neurons. The AAS model is\nhence well suited for theoretical studies of nearly critical brain dynamics. We\nalso point out that the waiting-time distribution allows an avalanche-free\nexperimental access to criticality.", "category": "cond-mat_dis-nn" }, { "text": "Single crystal growth and study of the magnetic properties of the mixed\n spin-dimer system Ba$_{3-x}$Sr$_{x}$Cr$_{2}$O$_{8}$: The compounds Sr$_{3}$Cr$_{2}$O$_{8}$ and Ba$_{3}$Cr$_{2}$O$_{8}$ are\ninsulating dimerized antiferromagnets with Cr$^{5+}$ magnetic ions. These\nspin-$\\frac{1}{2}$ ions form hexagonal bilayers with a strong intradimer\nantiferromagnetic interaction, that leads to a singlet ground state and gapped\ntriplet states. We report on the effect on the magnetic properties of\nSr$_{3}$Cr$_{2}$O$_{8}$ by introducing chemical disorder upon replacing Sr by\nBa. Two single crystals of Ba$_{3-x}$Sr$_{x}$Cr$_{2}$O$_{8}$ with $x=2.9$\n(3.33\\% of $mixing$) and $x=2.8$ (6.66\\%) were grown in a four-mirror type\noptical floating-zone furnace. The magnetic properties on these compounds were\nstudied by magnetization measurements. Inelastic neutron scattering\nmeasurements on Ba$_{0.1}$Sr$_{2.9}$Cr$_{2}$O$_{8}$ were performed in order to\ndetermine the interaction constants and the spin gap for $x=2.9$. The\nintradimer interaction constant is found to be $J_0$=5.332(2) meV, about 4\\%\nsmaller than that of pure Sr$_{3}$Cr$_{2}$O$_{8}$, while the interdimer\nexchange interaction $J_e$ is smaller by 6.9\\%. These results indicate a\nnoticeable change in the magnetic properties by a random substitution effect.", "category": "cond-mat_dis-nn" }, { "text": "Selberg integrals in 1D random Euclidean optimization problems: We consider a set of Euclidean optimization problems in one dimension, where\nthe cost function associated to the couple of points $x$ and $y$ is the\nEuclidean distance between them to an arbitrary power $p\\ge1$, and the points\nare chosen at random with flat measure. We derive the exact average cost for\nthe random assignment problem, for any number of points, by using Selberg's\nintegrals. Some variants of these integrals allows to derive also the exact\naverage cost for the bipartite travelling salesman problem.", "category": "cond-mat_dis-nn" }, { "text": "Inflation versus projection sets in aperiodic systems: The role of the\n window in averaging and diffraction: Tilings based on the cut and project method are key model systems for the\ndescription of aperiodic solids. Typically, quantities of interest in\ncrystallography involve averaging over large patches, and are well defined only\nin the infinite-volume limit. In particular, this is the case for\nautocorrelation and diffraction measures. For cut and project systems, the\naveraging can conveniently be transferred to internal space, which means\ndealing with the corresponding windows. We illustrate this by the example of\naveraged shelling numbers for the Fibonacci tiling and review the standard\napproach to the diffraction for this example. Further, we discuss recent\ndevelopments for inflation-symmetric cut and project structures, which are\nbased on an internal counterpart of the renormalisation cocycle. Finally, we\nbriefly review the notion of hyperuniformity, which has recently gained\npopularity, and its application to aperiodic structures.", "category": "cond-mat_dis-nn" }, { "text": "The complex dynamics of memristive circuits: analytical results and\n universal slow relaxation: Networks with memristive elements (resistors with memory) are being explored\nfor a variety of applications ranging from unconventional computing to models\nof the brain. However, analytical results that highlight the role of the graph\nconnectivity on the memory dynamics are still a few, thus limiting our\nunderstanding of these important dynamical systems. In this paper, we derive an\nexact matrix equation of motion that takes into account all the network\nconstraints of a purely memristive circuit, and we employ it to derive\nanalytical results regarding its relaxation properties. We are able to describe\nthe memory evolution in terms of orthogonal projection operators onto the\nsubspace of fundamental loop space of the underlying circuit. This orthogonal\nprojection explicitly reveals the coupling between the spatial and temporal\nsectors of the memristive circuits and compactly describes the circuit\ntopology. For the case of disordered graphs, we are able to explain the\nemergence of a power law relaxation as a superposition of exponential\nrelaxation times with a broad range of scales using random matrices. This power\nlaw is also {\\it universal}, namely independent of the topology of the\nunderlying graph but dependent only on the density of loops. In the case of\ncircuits subject to alternating voltage instead, we are able to obtain an\napproximate solution of the dynamics, which is tested against a specific\nnetwork topology. These result suggest a much richer dynamics of memristive\nnetworks than previously considered.", "category": "cond-mat_dis-nn" }, { "text": "Spin Glasses: An introduction and overview is given of the theory of spin glasses and its\napplication.", "category": "cond-mat_dis-nn" }, { "text": "Spatio-temporal correlations in Wigner molecules: The dynamical response of Coulomb-interacting particles in nano-clusters are\nanalyzed at different temperatures characterizing their solid- and liquid-like\nbehavior. Depending on the trap-symmetry, both the spatial and temporal\ncorrelations undergo slow, stretched exponential relaxations at long times,\narising from spatially correlated motion in string-like paths. Our results\nindicate that the distinction between the `solid' and `liquid' is soft: While\nparticles in a `solid' flow producing dynamic heterogeneities, motion in\n`liquid' yields unusually long tail in the distribution of\nparticle-displacements. A phenomenological model captures much of the\nsubtleties of our numerical simulations.", "category": "cond-mat_dis-nn" }, { "text": "Phase Ordering and Onset of Collective Behavior in Chaotic Coupled Map\n Lattices: The phase ordering properties of lattices of band-chaotic maps coupled\ndiffusively with some coupling strength $g$ are studied in order to determine\nthe limit value $g_e$ beyond which multistability disappears and non-trivial\ncollective behavior is observed. The persistence of equivalent discrete spin\nvariables and the characteristic length of the patterns observed scale\nalgebraically with time during phase ordering. The associated exponents vary\ncontinuously with $g$ but remain proportional to each other, with a ratio close\nto that of the time-dependent Ginzburg-Landau equation. The corresponding\nindividual values seem to be recovered in the space-continuous limit.", "category": "cond-mat_dis-nn" }, { "text": "Fate of Quadratic Band Crossing under quasiperiodic modulation: We study the fate of two-dimensional quadratic band crossing topological\nphases under a one-dimensional quasiperiodic modulation. By employing\nnumerically exact methods, we fully characterize the phase diagram of the model\nin terms of spectral, localization and topological properties. Unlike in the\npresence of regular disorder, the quadratic band crossing is stable towards the\napplication of the quasiperiodic potential and most of the topological phase\ntransitions occur through a gap closing and reopening mechanism, as in the\nhomogeneous case. With a sufficiently strong quasiperiodic potential, the\nquadratic band crossing point splits into Dirac cones which enables transitions\ninto gapped phases with Chern numbers $C=\\pm1$, absent in the homogeneous\nlimit. This is in sharp contrast with the disordered case, where gapless\n$C=\\pm1$ phases can arise by perturbing the band crossing with any amount of\ndisorder. In the quasiperiodic case, we find that the $C=\\pm1$ phases can only\nbecome gapless for a very strong potential. Only in this regime, the subsequent\nquasiperiodic-induced topological transitions into the trivial phase mirror the\nwell-known ``levitation and annihilation'' mechanism in the disordered case.", "category": "cond-mat_dis-nn" }, { "text": "Quantum Annealing: from Viewpoints of Statistical Physics, Condensed\n Matter Physics, and Computational Physics: In this paper, we review some features of quantum annealing and related\ntopics from viewpoints of statistical physics, condensed matter physics, and\ncomputational physics. We can obtain a better solution of optimization problems\nin many cases by using the quantum annealing. Actually the efficiency of the\nquantum annealing has been demonstrated for problems based on statistical\nphysics. Then the quantum annealing has been expected to be an efficient and\ngeneric solver of optimization problems. Since many implementation methods of\nthe quantum annealing have been developed and will be proposed in the future,\ntheoretical frameworks of wide area of science and experimental technologies\nwill be evolved through studies of the quantum annealing.", "category": "cond-mat_dis-nn" }, { "text": "Power law hopping of single particles in one-dimensional non-Hermitian\n quasicrystals: In this paper, a non-Hermitian Aubry-Andr\\'e-Harper model with power-law\nhoppings ($1/s^{a}$) and quasiperiodic parameter $\\beta$ is studied, where $a$\nis the power-law index, $s$ is the hopping distance, and $\\beta$ is a member of\nthe metallic mean family. We find that under the weak non-Hermitian effect,\nthere preserves $P_{\\ell=1,2,3,4}$ regimes where the fraction of ergodic\neigenstates is $\\beta$-dependent as $\\beta^{\\ell}$L ($L$ is the system size)\nsimilar to those in the Hermitian case. However, $P_{\\ell}$ regimes are ruined\nby the strong non-Hermitian effect. Moreover, by analyzing the fractal\ndimension, we find that there are two types of edges aroused by the power-law\nindex $a$ in the single-particle spectrum, i.e., an ergodic-to-multifractal\nedge for the long-range hopping case ($a<1$), and an ergodic-to-localized edge\nfor the short-range hopping case ($a>1$). Meanwhile, the existence of these two\ntypes of edges is found to be robust against the non-Hermitian effect. By\nemploying the Simon-Spence theory, we analyzed the absence of the localized\nstates for $a<1$. For the short-range hopping case, with the Avila's global\ntheory and the Sarnak method, we consider a specific example with $a=2$ to\nreveal the presence of the intermediate phase and to analytically locate the\nintermediate regime and the ergodic-to-multifractal edge, which are\nself-consistent with the numerically results.", "category": "cond-mat_dis-nn" }, { "text": "Universal spectral form factor for many-body localization: We theoretically study correlations present deep in the spectrum of\nmany-body-localized systems. An exact analytical expression for the spectral\nform factor of Poisson spectra can be obtained and is shown to agree well with\nnumerical results on two models exhibiting many-body-localization: a disordered\nquantum spin chain and a phenomenological $l$-bit model based on the existence\nof local integrals of motion. We also identify a universal regime that is\ninsensitive to the global density of states as well as spectral edge effects.", "category": "cond-mat_dis-nn" }, { "text": "Wannier band transitions in disordered $\u03c0$-flux ladders: Boundary obstructed topological insulators are an unusual class of\nhigher-order topological insulators with topological characteristics determined\nby the so-called Wannier bands. Boundary obstructed phases can harbor\nhinge/corner modes, but these modes can often be destabilized by a phase\ntransition on the boundary instead of the bulk. While there has been much work\non the stability of topological insulators in the presence disorder, the\ntopology of a disordered Wannier band, and disorder-induced Wannier transitions\nhave not been extensively studied. In this work, we focus on the simplest\nexample of a Wannier topological insulator: a mirror-symmetric $\\pi$-flux\nladder in 1D. We find that the Wannier topology is robust to disorder, and\nderive a real-space renormalization group procedure to understand a new type of\nstrong disorder-induced transition between non-trivial and trivial Wannier\ntopological phases. We also establish a connection between the Wannier topology\nof the ladder and the energy band topology of a related system with a physical\nboundary cut, something which has generally been conjectured for clean models,\nbut has not been studied in the presence of disorder.", "category": "cond-mat_dis-nn" }, { "text": "Criticality and Chaos in Systems of Communities: We consider a simple model of communities interacting via bilinear terms.\nAfter analyzing the thermal equilibrium case, which can be described by an\nHamiltonian, we introduce the dynamics that, for Ising-like variables, reduces\nto a Glauber-like dynamics. We analyze and compare four different versions of\nthe dynamics: flow (differential equations), map (discrete-time dynamics),\nlocal-time update flow, and local-time update map. The presence of only\nbilinear interactions prevent the flow cases to develop any dynamical\ninstability, the system converging always to the thermal equilibrium. The\nsituation is different for the map when unfriendly couplings are involved,\nwhere period-two oscillations arise. In the case of the map with local-time\nupdates, oscillations of any period and chaos can arise as a consequence of the\nreciprocal \"tension\" accumulated among the communities during their sleeping\ntime interval. The resulting chaos can be of two kinds: true chaos\ncharacterized by positive Lyapunov exponent and bifurcation cascades, or\nmarginal chaos characterized by zero Lyapunov exponent and critical continuous\nregions.", "category": "cond-mat_dis-nn" }, { "text": "Simulation of multi-shell fullerenes using Machine-Learning Gaussian\n Approximation Potential: Multi-shell fullerenes \"buckyonions\" were simulated, starting from initially\nrandom configurations, using a density-functional-theory (DFT)-trained\nmachine-learning carbon potential within the Gaussian Approximation Potential\n(ML-GAP) Framework [Volker L. Deringer and Gabor Csanyi, Phys. Rev. B 95,\n094203 (2017)]. A large set of such fullerenes were obtained with sizes ranging\nfrom 60 ~ 3774 atoms. The buckyonions are formed by clustering and layering\nstarts from the outermost shell and proceed inward. Inter-shell cohesion is\npartly due to interaction between delocalized $\\pi$ electrons into the gallery.\nThe energies of the models were validated ex post facto using density\nfunctional codes, VASP and SIESTA, revealing an energy difference within the\nrange of 0.02 - 0.08 eV/atom after conjuagte gradient energy convergence of the\nmodels were achieved with both methods.", "category": "cond-mat_dis-nn" }, { "text": "Context-dependent representation in recurrent neural networks: In order to assess the short-term memory performance of non-linear random\nneural networks, we introduce a measure to quantify the dependence of a neural\nrepresentation upon the past context. We study this measure both numerically\nand theoretically using the mean-field theory for random neural networks,\nshowing the existence of an optimal level of synaptic weights heterogeneity. We\nfurther investigate the influence of the network topology, in particular the\nsymmetry of reciprocal synaptic connections, on this measure of context\ndependence, revealing the importance of considering the interplay between\nnon-linearities and connectivity structure.", "category": "cond-mat_dis-nn" }, { "text": "Signatures of Many-Body Localization in the Dynamics of Two-Level\n Systems in Glasses: We investigate the quantum dynamics of Two-Level Systems (TLS) in glasses at\nlow temperatures (1 K and below). We study an ensemble of TLSs coupled to\nphonons. By integrating out the phonons within the framework of the\nGorini-Kossakowski-Sudarshan-Lindblad (GKSL) master equation, we derive\nanalytically the explicit form of the interactions among TLSs, and of the\ndissipation terms. We find that the unitary dynamics of the system shows clear\nsignatures of Many-Body Localization physics. We study numerically the time\nbehavior of the concurrence, which measures pairwise entanglement also in\nnon-isolated systems, and show that it presents a power-law decay both in the\nabsence and in the presence of dissipation, if the latter is not too large.\nThese features can be ascribed to the strong, long-tailed disorder\ncharacterizing the distributions of the model parameters. Our findings show\nthat assuming ergodicity when discussing TLS physics might not be justified for\nall kinds of experiments on low-temperature glasses.", "category": "cond-mat_dis-nn" }, { "text": "Critical properties of the measurement-induced transition in random\n quantum circuits: We numerically study the measurement-driven quantum phase transition of\nHaar-random quantum circuits in $1+1$ dimensions. By analyzing the tripartite\nmutual information we are able to make a precise estimate of the critical\nmeasurement rate $p_c = 0.17(1)$. We extract estimates for the associated bulk\ncritical exponents that are consistent with the values for percolation, as well\nas those for stabilizer circuits, but differ from previous estimates for the\nHaar-random case. Our estimates of the surface order parameter exponent appear\ndifferent from that for stabilizer circuits or percolation, but we are unable\nto definitively rule out the scenario where all exponents in the three cases\nmatch. Moreover, in the Haar case the prefactor for the entanglement entropies\n$S_n$ depends strongly on the R\\'enyi index $n$; for stabilizer circuits and\npercolation this dependence is absent. Results on stabilizer circuits are used\nto guide our study and identify measures with weak finite-size effects. We\ndiscuss how our numerical estimates constrain theories of the transition.", "category": "cond-mat_dis-nn" }, { "text": "On the Effects of Changing the Boundary Conditions on the Ground State\n of Ising Spin Glasses: We compute and analyze couples of ground states of 3D spin glass systems with\nthe same quenched noise but periodic and anti-periodic boundary conditions for\ndifferent lattice sizes. We discuss the possible different behaviors of the\nsystem, we analyze the average link overlap, the probability distribution of\nwindow overlaps (among ground states computed with different boundary\nconditions) and the spatial overlap and link overlap correlation functions. We\nestablish that the picture based on Replica Symmetry Breaking correctly\ndescribes the behavior of 3D Spin Glasses.", "category": "cond-mat_dis-nn" }, { "text": "Comment on ``Both site and link overlap distributions are non trivial in\n 3-dimensional Ising spin glasses'', cond-mat/0608535v2: We comment on recent numerical experiments by G.Hed and E.Domany\n[cond-mat/0608535v2] on the quenched equilibrium state of the Edwards-Anderson\nspin glass model. The rigorous proof of overlap identities related to replica\nequivalence shows that the observed violations of those identities on finite\nsize systems must vanish in the thermodynamic limit. See also the successive\nversion cond-mat/0608535v4", "category": "cond-mat_dis-nn" }, { "text": "Intermittency of dynamical phases in a quantum spin glass: Answering the question of existence of efficient quantum algorithms for\nNP-hard problems require deep theoretical understanding of the properties of\nthe low-energy eigenstates and long-time coherent dynamics in quantum spin\nglasses. We discovered and described analytically the property of asymptotic\northogonality resulting in a new type of structure in quantum spin glass. Its\neigen-spectrum is split into the alternating sequence of bands formed by\nquantum states of two distinct types ($x$ and $z$). Those of $z$-type are\nnon-ergodic extended eigenstates (NEE) in the basis of $\\{\\sigma_z\\}$ operators\nthat inherit the structure of the classical spin glass with exponentially long\ndecay times of Edwards Anderson order parameter at any finite value of\ntransverse field $B_{\\perp}$. Those of $x$-type form narrow bands of NEEs that\nconserve the integer-valued $x$-magnetization. Quantum evolution within a given\nband of each type is described by a Hamiltonian that belongs to either the\nensemble of Preferred Basis Levi matrices ($z$-type) or Gaussian Orthogonal\nensemble ($x$-type). We characterize the non-equilibrium dynamics using fractal\ndimension $D$ that depends on energy density (temperature) and plays a role of\nthermodynamic potential: $D=0$ in MBL phase, $01/2$, the\nmodel belongs to the same universality class as its short-range variant. The\nentanglement entropy of a block of size $L$ increases logarithmically with $L$\nin the critical point but, as opposed to the short-range model, the prefactor\nis disorder-dependent in the range $0\\simL^{d_f}$ the growth of the average domain-wall length with %%\nsystems size $L\\times L$. %% 20.07.07 OM %% Exploring systems up to L=320 we\nyield $d_f=1.274(2)$ for the case of Gaussian disorder, i.e. a much higher\naccuracy compared to previous studies. For the case of bimodal disorder, where\nmany equivalent domain walls exist due to the degeneracy of this model, we\nobtain a true lower bound $d_f=1.095(2)$ and a (lower) estimate $d_f=1.395(3)$\nas upper bound. Furthermore, we study the distributions of the domain-wall\nlengths. Their scaling with system size can be described also only by the\nexponent $d_f$, i.e. the distributions are monofractal. Finally, we investigate\nthe growth of the domain-wall width with system size (``roughness'') and find a\nlinear behavior.", "category": "cond-mat_dis-nn" }, { "text": "Information propagation in isolated quantum systems: Entanglement growth and out-of-time-order correlators (OTOC) are used to\nassess the propagation of information in isolated quantum systems. In this\nwork, using large scale exact time-evolution we show that for weakly disordered\nnonintegrable systems information propagates behind a ballistically moving\nfront, and the entanglement entropy growths linearly in time. For stronger\ndisorder the motion of the information front is algebraic and sub-ballistic and\nis characterized by an exponent which depends on the strength of the disorder,\nsimilarly to the sublinear growth of the entanglement entropy. We show that the\ndynamical exponent associated with the information front coincides with the\nexponent of the growth of the entanglement entropy for both weak and strong\ndisorder. We also demonstrate that the temporal dependence of the OTOC is\ncharacterized by a fast\\emph onnonexponential\\emph default growth, followed by\na slow saturation after the passage of the information front. Finally,we\ndiscuss the implications of this behavioral change on the growth of the\nentanglement entropy.", "category": "cond-mat_dis-nn" }, { "text": "The unreasonable effectiveness of tree-based theory for networks with\n clustering: We demonstrate that a tree-based theory for various dynamical processes\nyields extremely accurate results for several networks with high levels of\nclustering. We find that such a theory works well as long as the mean\nintervertex distance $\\ell$ is sufficiently small - i.e., as long as it is\nclose to the value of $\\ell$ in a random network with negligible clustering and\nthe same degree-degree correlations. We confirm this hypothesis numerically\nusing real-world networks from various domains and on several classes of\nsynthetic clustered networks. We present analytical calculations that further\nsupport our claim that tree-based theories can be accurate for clustered\nnetworks provided that the networks are \"sufficiently small\" worlds.", "category": "cond-mat_dis-nn" }, { "text": "Energy transport in a disordered spin chain with broken U(1) symmetry:\n Diffusion, subdiffusion, and many-body localization: We explore the physics of the disordered XYZ spin chain using two\ncomplementary numerical techniques: exact diagonalization (ED) on chains of up\nto 17 spins, and time-evolving block decimation (TEBD) on chains of up to 400\nspins. Our principal findings are as follows. First, the clean XYZ spin chain\nshows ballistic energy transport for all parameter values that we investigated.\nSecond, for weak disorder there is a stable diffusive region that persists up\nto a critical disorder strength that depends on the XY anisotropy. Third, for\ndisorder strengths above this critical value energy transport becomes\nincreasingly subdiffusive. Fourth, the many-body localization transition moves\nto significantly higher disorder strengths as the XY anisotropy is increased.\nWe discuss these results, and their relation to our current physical picture of\nsubdiffusion in the approach to many-body localization.", "category": "cond-mat_dis-nn" }, { "text": "Competitive cluster growth in complex networks: Understanding the process by which the individuals of a society make up their\nminds and reach opinions about different issues can be of fundamental\nimportance. In this work we propose an idealized model for competitive cluster\ngrowth in complex networks. Each cluster can be thought as a fraction of a\ncommunity that shares some common opinion. Our results show that the cluster\nsize distribution depends on the particular choice for the topology of the\nnetwork of contacts among the agents. As an application, we show that the\ncluster size distributions obtained when the growth process is performed on\nhierarchical networks, e.g., the Apollonian network, have a scaling form\nsimilar to what has been observed for the distribution of number of votes in an\nelectoral process. We suggest that this similarity is due to the fact that\nsocial networks involved in the electoral process may also posses an\nunderlining hierarchical structure.", "category": "cond-mat_dis-nn" }, { "text": "Classical magnetotransport of inhomogeneous conductors: We present a model of magnetotransport of inhomogeneous conductors based on\nan array of coupled four-terminal elements. We show that this model generically\nyields non-saturating magnetoresistance at large fields. We also discuss how\nthis approach simplifies finite-element analysis of bulk inhomogeneous\nsemiconductors in complex geometries. We argue that this is an explanation of\nthe observed non-saturating magnetoresistance in silver chalcogenides and\npotentially in other disordered conductors. Our method may be used to design\nthe magnetoresistive response of a microfabricated array.", "category": "cond-mat_dis-nn" }, { "text": "Phase Diagram of mixed bond Ising systems by use of Monte Carlo and the\n effective-field theory: The phase transition of a random mixed-bond Ising ferromagnet on a cubic\nlattice model is studied both numerically and analytically. In this work, we\nuse the Cluster algorithms of Wolff and Glauber to simulate the dynamics of the\nsystem. We obtained the thermodynamic quantities such as magnetization,\nsusceptibility, and specific heat. Our results were compared with those\nobtained using a new technique in effective field theory that employs similar\nprobability distribution within the framework of two-site clusters", "category": "cond-mat_dis-nn" }, { "text": "Statistics of energy levels and eigenfunctions in disordered and chaotic\n systems: Supersymmetry approach: The supersymmetry method has proven to be a very powerful tool of study of\nthe statistical properties of energy levels and eigenfunctions in disordered\nand chaotic systems. The aim of these lectures is to present a tutorial\nintroduction to the method, as well as an overview of the recent developments.", "category": "cond-mat_dis-nn" }, { "text": "Improved algorithm for neuronal ensemble inference by Monte Carlo method: Neuronal ensemble inference is one of the significant problems in the study\nof biological neural networks. Various methods have been proposed for ensemble\ninference from their activity data taken experimentally. Here we focus on\nBayesian inference approach for ensembles with generative model, which was\nproposed in recent work. However, this method requires large computational\ncost, and the result sometimes gets stuck in bad local maximum solution of\nBayesian inference. In this work, we give improved Bayesian inference algorithm\nfor these problems. We modify ensemble generation rule in Markov chain Monte\nCarlo method, and introduce the idea of simulated annealing for hyperparameter\ncontrol. We also compare the performance of ensemble inference between our\nalgorithm and the original one.", "category": "cond-mat_dis-nn" }, { "text": "Molecular neuron based on the Franck-Condon blockade: Electronic realizations of neurons are of great interest as building blocks\nfor neuromorphic computation. Electronic neurons should send signals into the\ninput and output lines when subject to an input signal exceeding a given\nthreshold, in such a way that they may affect all other parts of a neural\nnetwork. Here, we propose a design for a neuron that is based on\nmolecular-electronics components and thus promises a very high level of\nintegration. We employ the Monte Carlo technique to simulate typical time\nevolutions of this system and thereby show that it indeed functions as a\nneuron.", "category": "cond-mat_dis-nn" }, { "text": "Apparent slow dynamics in the ergodic phase of a driven many-body\n localized system without extensive conserved quantities: We numerically study the dynamics on the ergodic side of the many-body\nlocalization transition in a periodically driven Floquet model with no global\nconservation laws. We describe and employ a numerical technique based on the\nfast Walsh-Hadamard transform that allows us to perform an exact time evolution\nfor large systems and long times. As in models with conserved quantities (e.g.,\nenergy and/or particle number) we observe a slowing down of the dynamics as the\ntransition into the many-body localized phase is approached. More specifically,\nour data is consistent with a subballistic spread of entanglement and a\nstretched-exponential decay of an autocorrelation function, with their\nassociated exponents reflecting slow dynamics near the transition for a fixed\nsystem size. However, with access to larger system sizes, we observe a clear\nflow of the exponents towards faster dynamics and can not rule out that the\nslow dynamics is a finite-size effect. Furthermore, we observe examples of\nnon-monotonic dependence of the exponents with time, with dynamics initially\nslowing down but accelerating again at even larger times, consistent with the\nslow dynamics being a crossover phenomena with a localized critical point.", "category": "cond-mat_dis-nn" }, { "text": "One step replica symmetry breaking and overlaps between two temperatures: We obtain an exact analytic expression for the average distribution, in the\nthermodynamic limit, of overlaps between two copies of the same random energy\nmodel (REM) at different temperatures. We quantify the non-self averaging\neffects and provide an exact approach to the computation of the fluctuations in\nthe distribution of overlaps in the thermodynamic limit. We show that the\noverlap probabilities satisfy recurrence relations that generalise\nGhirlanda-Guerra identities to two temperatures.\n We also analyse the two temperature REM using the replica method. The replica\nexpressions for the overlap probabilities satisfy the same recurrence relations\nas the exact form. We show how a generalisation of Parisi's replica symmetry\nbreaking ansatz is consistent with our replica expressions. A crucial aspect to\nthis generalisation is that we must allow for fluctuations in the replica block\nsizes even in the thermodynamic limit. This contrasts with the single\ntemperature case where the extremal condition leads to a fixed block size in\nthe thermodynamic limit. Finally, we analyse the fluctuations of the block\nsizes in our generalised Parisi ansatz and show that in general they may have a\nnegative variance.", "category": "cond-mat_dis-nn" }, { "text": "A conjectured scenario for order-parameter fluctuations in spin glasses: We study order-parameter fluctuations (OPF) in disordered systems by\nconsidering the behavior of some recently introduced paramaters $G,G_c$ which\nhave proven very useful to locate phase transitions. We prove that both\nparameters G (for disconnected overlap disorder averages) and $G_c$ (for\nconnected disorder averages) take the respective universal values 1/3 and 13/31\nin the $T\\to 0$ limit for any {\\em finite} volume provided the ground state is\n{\\em unique} and there is no gap in the ground state local-field distributions,\nconditions which are met in generic spin-glass models with continuous couplings\nand no gap at zero coupling. This makes $G,G_c$ ideal parameters to locate\nphase transitions in disordered systems much alike the Binder cumulant is for\nordered systems. We check our results by exactly computing OPF in a simple\nexample of uncoupled spins in the presence of random fields and the\none-dimensional Ising spin glass. At finite temperatures, we discuss in which\nconditions the value 1/3 for G may be recovered by conjecturing different\nscenarios depending on whether OPF are finite or vanish in the infinite-volume\nlimit. In particular, we discuss replica equivalence and its natural\nconsequence $\\lim_{V\\to\\infty}G(V,T)=1/3$ when OPF are finite. As an example of\na model where OPF vanish and replica equivalence does not give information\nabout G we study the Sherrington-Kirkpatrick spherical spin-glass model by\ndoing numerical simulations for small sizes. Again we find results compatible\nwith G=1/3 in the spin-glass phase.", "category": "cond-mat_dis-nn" }, { "text": "Experimental study of the effect of disorder on subcritical crack growth\n dynamics: The growth dynamics of a single crack in a heterogeneous material under\nsubcritical loading is an intermittent process; and many features of this\ndynamics have been shown to agree with simple models of thermally activated\nrupture. In order to better understand the role of material heterogeneities in\nthis process, we study the subcritical propagation of a crack in a sheet of\npaper in the presence of a distribution of small defects such as holes. The\nexperimental data obtained for two different distributions of holes are\ndiscussed in the light of models that predict the slowing down of crack growth\nwhen the disorder in the material is increased; however, in contradiction with\nthese theoretical predictions, the experiments result in longer lasting cracks\nin a more ordered scenario. We argue that this effect is specific to\nsubcritical crack dynamics and that the weakest zones between holes at close\ndistance to each other are responsible both for the acceleration of the crack\ndynamics and the slightly different roughness of the crack path.", "category": "cond-mat_dis-nn" }, { "text": "A statistical-mechanical approach to CDMA multiuser detection:\n propagating beliefs in a densely connected graph: The task of CDMA multiuser detection is to simultaneously estimate binary\nsymbols of $K$ synchronous users from the received $N$ base-band CDMA signals.\nMathematically, this can be formulated as an inference problem on a complete\nbipartite graph. In the research on graphically represented statistical models,\nit is known that the belief propagation (BP) can exactly perform the inference\nin a polynomial time scale of the system size when the graph is free from\ncycles in spite that the necessary computation for general graphs exponentially\nexplodes in the worst case. In addition, recent several researches revealed\nthat the BP can also serve as an excellent approximation algorithm even if the\ngraph has cycles as far as they are relatively long. However, as there exit\nmany short cycles in a complete bipartite graph, one might suspect that the BP\nwould not provide a good performance when employed for the multiuser detection.\n The purpose of this paper is to make an objection to such suspicion. More\nspecifically, we will show that appropriate employment of the central limit\ntheorem and the law of large numbers to BP, which is one of the standard\ntechniques in statistical mechanics, makes it possible to develop a novel\nmultiuser detection algorithm the convergence property of which is considerably\nbetter than that of the conventional multistage detection without increasing\nthe computational cost significantly. Furthermore, we will also provide a\nscheme to analyse the dynamics of the proposed algorithm, which can be\nnaturally linked to the equilibrium analysis recently presented by Tanaka.", "category": "cond-mat_dis-nn" }, { "text": "Chemical order lifetimes in liquids in the energy landscape paradigm: Recent efforts to deal with the complexities of the liquid state,\nparticularly those of glassforming systems, have focused on the \"energy\nlandscape\" as a means of dealing with the collective variables problem [1]. The\n\"basins of attraction\" that constitute the landscape features in configuration\nspace represent a distinct class of microstates of the system. So far only the\nmicrostates that are related to structural relaxation and viscosity have been\nconsidered in this paradigm. But most of the complex systems of importance in\nnature and industry are solutions, particularly solutions that are highly\nnon-ideal in character. In these, a distinct class of fluctuations exists, the\nfluctuations in concentration. The mean square amplitudes of these fluctuations\nrelate to the chemical activity coefficients [2], and their rise and decay\ntimes may be much longer than those of the density fluctuations - from which\nthey may be statistically independent. Here we provide data on the character of\nchemical order fluctuations in viscous liquids and on their relation to the\nenthalpy fluctuations that determine the structural relaxation time, and hence\nthe glass temperature Tg. Using a spectroscopically active chemical order\nprobe, we identify a \"chemical fictive temperature\", Tchm, by analogy with the\nfamiliar \"fictive temperature\" Tf (the cooling Tg). Like Tf, Tchm must be the\nsame as the real temperature for the system to be in complete equilibrium. It\nis possible for mobile multicomponent liquids to be permanently nonergodic,\ninsofar as Tchm > Tf = T, which must be accommodated within the landscape\nparadigm. We note that, in appropriate systems, an increase in concentration of\nslow chemically ordering units in liquids can produce a crossover to fast ion\nconducting glass phenomenology.", "category": "cond-mat_dis-nn" }, { "text": "Analytic Solution to Clustering Coefficients on Weighted Networks: Clustering coefficient is an important topological feature of complex\nnetworks. It is, however, an open question to give out its analytic expression\non weighted networks yet. Here we applied an extended mean-field approach to\ninvestigate clustering coefficients in the typical weighted networks proposed\nby Barrat, Barth\\'elemy and Vespignani (BBV networks). We provide analytical\nsolutions of this model and find that the local clustering in BBV networks\ndepends on the node degree and strength. Our analysis is well in agreement with\nresults of numerical simulations.", "category": "cond-mat_dis-nn" }, { "text": "Water Droplet Avalanches: We analyze the statistics of water droplet avalanches in a continuously\ndriven system. Distributions are obtained for avalanche size, lifetime, and\ntime between successive avalanches, along with power spectra and return maps.\nFor low flow rates and different water viscosities, we observe a power-law\nscaling in the size and lifetime distributions of water droplet avalanches,\nindicating that a state with no characteristic time and length scales was\nreached. Higher flow rates resulted in an exponential behavior with\ncharacteristic scales.", "category": "cond-mat_dis-nn" }, { "text": "Structural and Energetic Heterogeneity in Protein Folding: A general theoretical framework is developed using free energy functional\nmethods to understand the effects of heterogeneity in the folding of a\nwell-designed protein. Native energetic heterogeneity arising from\nnon-uniformity in native stability, as well as entropic heterogeneity intrinsic\nto the topology of the native structure are both investigated as to their\nimpact on the folding free energy landscape and resulting folding mechanism.\nGiven a minimally frustrated protein, both structural and energetic\nheterogeneity lower the thermodynamic barrier to folding, and designing in\nsufficient heterogeneity can eliminate the barrier at the folding transition\ntemperature. Sequences with different distributions of stability throughout the\nprotein and correspondingly different folding mechanisms may still be good\nfolders to the same structure. This theoretical framework allows for a\nsystematic study of the coupled effects of energetics and topology in protein\nfolding, and provides interpretations and predictions for future experiments\nwhich may investigate these effects.", "category": "cond-mat_dis-nn" }, { "text": "Spin-charge separation and many-body localization: We study many-body localization for a disordered chain of spin 1/2 fermions.\nIn [Phys. Rev. B \\textbf{94}, 241104 (2016)], when both down and up components\nare exposed to the same strong disorder, the authors observe a power law growth\nof the entanglement entropy that suggests that many-body localization is not\ncomplete; the density (charge) degree of freedom is localized, while the spin\ndegree of freedom is apparently delocalized. We show that this power-like\nbehavior is only a transient effect and that, for longer times, the growth is\nlogarithmic in time suggesting that the spin degree of freedom is also\nlocalized, so that the system follows the standard many-body localization\nscenario. We also study the experimentally relevant case of quasiperiodic\ndisorder.", "category": "cond-mat_dis-nn" }, { "text": "Stretched Exponential Relaxation on the Hypercube and the Glass\n Transition: We study random walks on the dilute hypercube using an exact enumeration\nMaster equation technique, which is much more efficient than Monte Carlo\nmethods for this problem. For each dilution $p$ the form of the relaxation of\nthe memory function $q(t)$ can be accurately parametrized by a stretched\nexponential $q(t)=\\exp(-(t/\\tau)^\\beta)$ over several orders of magnitude in\n$q(t)$. As the critical dilution for percolation $p_c$ is approached, the time\nconstant $\\tau(p)$ tends to diverge and the stretching exponent $\\beta(p)$\ndrops towards 1/3. As the same pattern of relaxation is observed in wide class\nof glass formers, the fractal like morphology of the giant cluster in the\ndilute hypercube is a good representation of the coarse grained phase space in\nthese systems. For these glass formers the glass transition can be pictured as\na percolation transition in phase space.", "category": "cond-mat_dis-nn" }, { "text": "Exciton Dephasing and Thermal Line Broadening in Molecular Aggregates: Using a model of Frenkel excitons coupled to a bath of acoustic phonons in\nthe host medium, we study the temperature dependence of the dephasing rates and\nhomogeneous line width in linear molecular aggregates. The model includes\nlocalization by disorder and predicts a power-law thermal scaling of the\neffective homogeneous line width. The theory gives excellent agreement with\ntemperature dependent absorption and hole-burning experiments on aggregates of\nthe dye pseudoisocyanine.", "category": "cond-mat_dis-nn" }, { "text": "Aging dynamics of ferromagnetic and reentrant spin glass phases in\n stage-2 Cu$_{0.80}$C$_{0.20}$Cl$_{2}$ graphite intercalation compound: Aging dynamics of a reentrant ferromagnet stage-2\nCu$_{0.8}$Co$_{0.2}$Cl$_{2}$ graphite intercalation compound has been studied\nusing DC magnetic susceptibility. This compound undergoes successive\ntransitions at the transition temperatures $T_{c}$ ($\\approx 8.7$ K) and\n$T_{RSG}$ ($\\approx 3.3$ K). The relaxation rate $S_{ZFC}(t)$ exhibits a\ncharacteristic peak at $t_{cr}$ below $T_{c}$. The peak time $t_{cr}$ as a\nfunction of temperature $T$ shows a local maximum around 5.5 K, reflecting a\nfrustrated nature of the ferromagnetic phase. It drastically increases with\ndecreasing temperature below $T_{RSG}$. The spin configuration imprinted at the\nstop and wait process at a stop temperature $T_{s}$ ($$), normalized magnetic field $h$\n($=H/H_{K}$), and the width $\\sigma$ of the log-normal distribution of the\nvolumes of nanoparticles, based on the superparamagnetic blocking model with no\ninteraction between the nanoparticles. Here $$ is the average volume,\n$K_{u}$ is the anisotropy energy, and $H_{K}$ is the anisotropy field. Main\nfeatures of the experimental results reported in many SPM's can be well\nexplained in terms of the present model. The normalized FC susceptibility\nincreases monotonically increases as the normalized temperature $y$ decreases.\nThe normalized ZFC susceptibility exhibits a peak at the normalized blocking\ntemperature $y_{b}$ ($=k_{B}T_{b}/K_{u}< V>$), forming the $y_{b}$ vs $h$\ndiagram. For large $\\sigma$ ($\\sigma >0.4$), $y_{b}$ starts to increase with\nincreasing $h$, showing a peak at $h=h_{b}$, and decreases with further\nincreasing $h$. The maximum of $y_{b}$ at $h=h_{b}$ is due to the nonlinearity\nof the Langevin function. For small $\\sigma$, $y_{b}$ monotonically decreases\nwith increasing $h$. The derivative of the normalized FC magnetization with\nrespect to $h$ shows a peak at $h$ = 0 for small $y$. This is closely related\nto the pinched form of $M_{FC}$ vs $H$ curve around $H$ = 0 observed in SPM's.", "category": "cond-mat_dis-nn" }, { "text": "Population spiking and bursting in next generation neural masses with\n spike-frequency adaptation: Spike-frequency adaptation (SFA) is a fundamental neuronal mechanism taking\ninto account the fatigue due to spike emissions and the consequent reduction of\nthe firing activity. We have studied the effect of this adaptation mechanism on\nthe macroscopic dynamics of excitatory and inhibitory networks of quadratic\nintegrate-and-fire (QIF) neurons coupled via exponentially decaying\npost-synaptic potentials. In particular, we have studied the population\nactivities by employing an exact mean field reduction, which gives rise to next\ngeneration neural mass models. This low-dimensional reduction allows for the\nderivation of bifurcation diagrams and the identification of the possible\nmacroscopic regimes emerging both in a single and in two identically coupled\nneural masses. In single populations SFA favours the emergence of population\nbursts in excitatory networks, while it hinders tonic population spiking for\ninhibitory ones. The symmetric coupling of two neural masses, in absence of\nadaptation, leads to the emergence of macroscopic solutions with broken\nsymmetry: namely, chimera-like solutions in the inhibitory case and anti-phase\npopulation spikes in the excitatory one. The addition of SFA leads to new\ncollective dynamical regimes exhibiting cross-frequency coupling (CFC) among\nthe fast synaptic time scale and the slow adaptation one, ranging from\nanti-phase slow-fast nested oscillations to symmetric and asymmetric bursting\nphenomena. The analysis of these CFC rhythms in the $\\theta$-$\\gamma$ range has\nrevealed that a reduction of SFA leads to an increase of the $\\theta$ frequency\njoined to a decrease of the $\\gamma$ one. This is analogous to what reported\nexperimentally for the hippocampus and the olfactory cortex of rodents under\ncholinergic modulation, that is known to reduce SFA.", "category": "cond-mat_dis-nn" }, { "text": "Algorithms for 3D rigidity analysis and a first order percolation\n transition: A fast computer algorithm, the pebble game, has been used successfully to\nstudy rigidity percolation on 2D elastic networks, as well as on a special\nclass of 3D networks, the bond-bending networks. Application of the pebble game\napproach to general 3D networks has been hindered by the fact that the\nunderlying mathematical theory is, strictly speaking, invalid in this case. We\nconstruct an approximate pebble game algorithm for general 3D networks, as well\nas a slower but exact algorithm, the relaxation algorithm, that we use for\ntesting the new pebble game. Based on the results of these tests and additional\nconsiderations, we argue that in the particular case of randomly diluted\ncentral-force networks on BCC and FCC lattices, the pebble game is essentially\nexact. Using the pebble game, we observe an extremely sharp jump in the largest\nrigid cluster size in bond-diluted central-force networks in 3D, with the\npercolating cluster appearing and taking up most of the network after a single\nbond addition. This strongly suggests a first order rigidity percolation\ntransition, which is in contrast to the second order transitions found\npreviously for the 2D central-force and 3D bond-bending networks. While a first\norder rigidity transition has been observed for Bethe lattices and networks\nwith ``chemical order'', this is the first time it has been seen for a regular\nrandomly diluted network. In the case of site dilution, the transition is also\nfirst order for BCC, but results for FCC suggest a second order transition.\nEven in bond-diluted lattices, while the transition appears massively first\norder in the order parameter (the percolating cluster size), it is continuous\nin the elastic moduli. This, and the apparent non-universality, make this phase\ntransition highly unusual.", "category": "cond-mat_dis-nn" }, { "text": "Spanning avalanches in the three-dimensional Gaussian Random Field Ising\n Model with metastable dynamics: field dependence and geometrical properties: Spanning avalanches in the 3D Gaussian Random Field Ising Model (3D-GRFIM)\nwith metastable dynamics at T=0 have been studied. Statistical analysis of the\nfield values for which avalanches occur has enabled a Finite-Size Scaling (FSS)\nstudy of the avalanche density to be performed. Furthermore, direct measurement\nof the geometrical properties of the avalanches has confirmed an earlier\nhypothesis that several kinds of spanning avalanches with two different fractal\ndimensions coexist at the critical point. We finally compare the phase diagram\nof the 3D-GRFIM with metastable dynamics with the same model in equilibrium at\nT=0.", "category": "cond-mat_dis-nn" }, { "text": "1/f Noise in Electron Glasses: We show that 1/f noise is produced in a 3D electron glass by charge\nfluctuations due to electrons hopping between isolated sites and a percolating\nnetwork at low temperatures. The low frequency noise spectrum goes as\n\\omega^{-\\alpha} with \\alpha slightly larger than 1. This result together with\nthe temperature dependence of \\alpha and the noise amplitude are in good\nagreement with the recent experiments. These results hold true both with a\nflat, noninteracting density of states and with a density of states that\nincludes Coulomb interactions. In the latter case, the density of states has a\nCoulomb gap that fills in with increasing temperature. For a large Coulomb gap\nwidth, this density of states gives a dc conductivity with a hopping exponent\nof approximately 0.75 which has been observed in recent experiments. For a\nsmall Coulomb gap width, the hopping exponent approximately 0.5.", "category": "cond-mat_dis-nn" }, { "text": "Nonequilibrium localization and the interplay between disorder and\n interactions: We study the nonequilibrium interplay between disorder and interactions in a\nclosed quantum system. We base our analysis on the notion of dynamical\nstate-space localization, calculated via the Loschmidt echo. Although\nreal-space and state-space localization are independent concepts in general, we\nshow that both perspectives may be directly connected through a specific choice\nof initial states, namely, maximally localized states (ML-states). We show\nnumerically that in the noninteracting case the average echo is found to be\nmonotonically increasing with increasing disorder; these results are in\nagreement with an analytical evaluation in the single particle case in which\nthe echo is found to be inversely proportional to the localization length. We\nalso show that for interacting systems, the length scale under which\nequilibration may occur is upper bounded and such bound is smaller the greater\nthe average echo of ML-states. When disorder and interactions, both being\nlocalization mechanisms, are simultaneously at play the echo features a\nnon-monotonic behaviour indicating a non-trivial interplay of the two\nprocesses. This interplay induces delocalization of the dynamics which is\naccompanied by delocalization in real-space. This non-monotonic behaviour is\nalso present in the effective integrability which we show by evaluating the gap\nstatistics.", "category": "cond-mat_dis-nn" }, { "text": "Vitrification of a monatomic 2D simple liquid: A monatomic simple liquid in two dimensions, where atoms interact\nisotropically through the Lennard-Jones-Gauss potential [M. Engel and H.-R.\nTrebin, Phys. Rev. Lett. 98, 225505 (2007)], is vitrified by the use of a rapid\ncooling technique in a molecular dynamics simulation. Transformation to a\ncrystalline state is investigated at various temperatures and the\ntime-temperature-transformation (TTT) curve is determined. It is found that the\ntransformation time to a crystalline state is the shortest at a temerature 14%\nbelow the melting temperature Tm and that at temperatures below Tv = 0.6 Tm the\ntransformation time is much longer than the available CPU time. This indicates\nthat a long-lived glassy state is realized for T < Tv.", "category": "cond-mat_dis-nn" }, { "text": "Hamiltonian equation of motion and depinning phase transition in\n two-dimensional magnets: Based on the Hamiltonian equation of motion of the $\\phi^4$ theory with\nquenched disorder, we investigate the depinning phase transition of the\ndomain-wall motion in two-dimensional magnets. With the short-time dynamic\napproach, we numerically determine the transition field, and the static and\ndynamic critical exponents. The results show that the fundamental Hamiltonian\nequation of motion belongs to a universality class very different from those\neffective equations of motion.", "category": "cond-mat_dis-nn" }, { "text": "Phase Singularity Diffusion: We follow the trajectories of phase singularities at nulls of intensity in\nthe speckle pattern of waves transmitted through random media as the frequency\nof the incident radiation is scanned in microwave experiments and numerical\nsimulations. Phase singularities are observed to diffuse with a linear increase\nof the square displacement with frequency shift. The product of the diffusion\ncoefficient of phase singularities in the transmitted speckle pattern and the\nphoton diffusion coefficient through the random medium is proportional to the\nsquare of the effective sample length. This provides the photon diffusion\ncoefficient and a method for characterizing the motion of dynamic material\nsystems.", "category": "cond-mat_dis-nn" }, { "text": "Thermal conductivity of molecular crystals with self-organizing disorder: The thermal conductivity of some orientational glasses of protonated C2H5OH\nand deuterated C2D5OD ethanol, cyclic substances (cyclohexanol C6H11OH,\ncyanocyclohexane C6H11CN, cyclohexene C6H10), and freon 112 (CFCl2)2 have been\nanalyzed in the temperature interval 2-130 K. The investigated substances\ndemonstrate new effects concerned with the physics of disordered systems.\nUniversal temperature dependences of the thermal conductivity of molecular\norientational glasses have been revealed. At low temperatures, the thermal\nconductivity exhibits a universal behavior that can be described by the soft\npotential model. At relatively high temperatures, the thermal conductivity has\na smeared maximum and than decreases with increase in the temperature, which\noccurs typically in crystalline structures.", "category": "cond-mat_dis-nn" }, { "text": "Critical Networks Exhibit Maximal Information Diversity in\n Structure-Dynamics Relationships: Network structure strongly constrains the range of dynamic behaviors\navailable to a complex system. These system dynamics can be classified based on\ntheir response to perturbations over time into two distinct regimes, ordered or\nchaotic, separated by a critical phase transition. Numerous studies have shown\nthat the most complex dynamics arise near the critical regime. Here we use an\ninformation theoretic approach to study structure-dynamics relationships within\na unified framework and how that these relationships are most diverse in the\ncritical regime.", "category": "cond-mat_dis-nn" }, { "text": "The plasmon-polariton mirroring due to strong fluctuations of the\n surface impedance: Scattering of TM-polarized surface plasmon-polariton waves (PPW) by a finite\nsegment of the metal-vacuum interface with randomly fluctuating surface\nimpedance is examined. Solution of the integral equation relating the scattered\nfield with the field of the incident PPW, valid for arbitrary scattering\nintensity and arbitrary dissipative characteristics of the conductive medium,\nis analyzed. As a measure of the PPW scattering, the Hilbert norm of the\nintegral scattering operator is used. The strength of the scattering is shown\nto be determined not only by the parameters of the fluctuating impedance\n(dispersion, correlation radius and the length of the inhomogeneity region) but\nalso by the conductivity of the metal. If the scattering operator norm is\nsmall, the PPW is mainly scattered into the vacuum, thus losing its energy\nthrough the excitation of quasi-isotropic bulk Norton-type waves above the\nconducting surface. The intensity of the scattered field is expressed in terms\nof the random impedance pair correlation function, whose dependence on the\nincident and scattered wavenumbers shows that in the case of\nrandom-impedance-induced scattering of PPW it is possible to observe the effect\nanalogous to Wood's anomalies of wave scattering on periodic gratings. Under\nstrong scattering, when the scattering operator norm becomes large compared to\nunity, the radiation into free space is strongly suppressed, and, in the limit,\nthe incoming PPW is almost perfectly back-reflected from the inhomogeneous part\nof the interface. This suggests that within the model of a dissipation-free\nconducting medium, the surface polariton is unstable against arbitrary small\nfluctuations of the medium polarizability. Transition from quasi-isotropic weak\nscattering to nealy back-reflection under strong fluctuations of the impedance\nis interpreted in terms of Anderson localization.", "category": "cond-mat_dis-nn" }, { "text": "Multifractal structure of Barkhausen noise: A signature of collective\n dynamics at hysteresis loop: The field-driven magnetisation reversal processes in disordered systems\nexhibit a collective behaviour that is manifested in the scale-invariance of\navalanches, closely related to underlying dynamical mechanisms. Using the\nmultifractal time series analysis, we study the structure of fluctuations at\ndifferent scales in the accompanying Barkhausen noise. The stochastic signal\nrepresents the magnetisation discontinuities along the hysteresis loop of a\n3-dimensional random field Ising model simulated for varied disorder strength\nand driving rates. The analysis of the spectrum of the generalised Hurst\nexponents reveals that the segments of the signal with large fluctuations\nrepresent two distinct classes of stochastic processes in weak and strong\npinning regimes. Furthermore, increased driving rates have a profound effect on\nthe small fluctuation segments and broadening of the spectrum. The study of the\ntemporal correlations, sequences of avalanches, and their scaling features\ncomplements the quantitative measures of the collective dynamics at the\nhysteresis loop. The multifractal properties of Barkhausen noise describe the\ndynamical state of domains and precisely discriminate the weak pinning,\npermitting the motion of individual walls, from the mechanisms occurring in\nstrongly disordered systems. The multifractal nature of the reversal processes\nis particularly relevant for currently investigated memory devices that utilize\na controlled motion of individual domain walls.", "category": "cond-mat_dis-nn" }, { "text": "Replacing neural networks by optimal analytical predictors for the\n detection of phase transitions: Identifying phase transitions and classifying phases of matter is central to\nunderstanding the properties and behavior of a broad range of material systems.\nIn recent years, machine-learning (ML) techniques have been successfully\napplied to perform such tasks in a data-driven manner. However, the success of\nthis approach notwithstanding, we still lack a clear understanding of ML\nmethods for detecting phase transitions, particularly of those that utilize\nneural networks (NNs). In this work, we derive analytical expressions for the\noptimal output of three widely used NN-based methods for detecting phase\ntransitions. These optimal predictions correspond to the results obtained in\nthe limit of high model capacity. Therefore, in practice they can, for example,\nbe recovered using sufficiently large, well-trained NNs. The inner workings of\nthe considered methods are revealed through the explicit dependence of the\noptimal output on the input data. By evaluating the analytical expressions, we\ncan identify phase transitions directly from experimentally accessible data\nwithout training NNs, which makes this procedure favorable in terms of\ncomputation time. Our theoretical results are supported by extensive numerical\nsimulations covering, e.g., topological, quantum, and many-body localization\nphase transitions. We expect similar analyses to provide a deeper understanding\nof other classification tasks in condensed matter physics.", "category": "cond-mat_dis-nn" }, { "text": "Universal spectral form factor for many-body localization: We theoretically study correlations present deep in the spectrum of\nmany-body-localized systems. An exact analytical expression for the spectral\nform factor of Poisson spectra can be obtained and is shown to agree well with\nnumerical results on two models exhibiting many-body-localization: a disordered\nquantum spin chain and a phenomenological $l$-bit model based on the existence\nof local integrals of motion. We also identify a universal regime that is\ninsensitive to the global density of states as well as spectral edge effects.", "category": "cond-mat_dis-nn" }, { "text": "Chaos and residual correlations in pinned disordered systems: We study, using functional renormalization (FRG), two copies of an elastic\nsystem pinned by mutually correlated random potentials. Short scale\ndecorrelation depend on a non trivial boundary layer regime with (possibly\nmultiple) chaos exponents. Large scale mutual displacement correlation behave\nas $|x-x'|^{2 \\zeta - \\mu}$, the decorrelation exponent $\\mu$ proportional to\nthe difference between Flory (or mean field) and exact roughness exponent\n$\\zeta$. For short range disorder $\\mu >0$ but small, e.g. for random bond\ninterfaces $\\mu = 5 \\zeta - \\epsilon$, $\\epsilon=4-d$, and $\\mu = \\epsilon\n(\\frac{(2 \\pi)^2}{36} - 1)$ for the one component Bragg glass. Random field\n(i.e long range) disorder exhibits finite residual correlations (no chaos $\\mu\n= 0$) described by new FRG fixed points. Temperature and dynamic chaos\n(depinning) are discussed.", "category": "cond-mat_dis-nn" }, { "text": "Energy distribution of maxima and minima in a one-dimensional random\n system: We study the energy distribution of maxima and minima of a simple\none-dimensional disordered Hamiltonian. We find that in systems with short\nrange correlated disorder there is energy separation between maxima and minima,\nsuch that at fixed energy only one kind of stationary points is dominant in\nnumber over the other. On the other hand, in the case of systems with long\nrange correlated disorder maxima and minima are completely mixed.", "category": "cond-mat_dis-nn" }, { "text": "Machine-learning assisted quantum control in random environment: Disorder in condensed matter and atomic physics is responsible for a great\nvariety of fascinating quantum phenomena, which are still challenging for\nunderstanding, not to mention the relevant dynamical control. Here we introduce\nproof of the concept and analyze neural network-based machine learning\nalgorithm for achieving feasible high-fidelity quantum control of a particle in\nrandom environment. To explicitly demonstrate its capabilities, we show that\nconvolutional neural networks are able to solve this problem as they can\nrecognize the disorder and, by supervised learning, further produce the policy\nfor the efficient low-energy cost control of a quantum particle in a\ntime-dependent random potential. We have shown that the accuracy of the\nproposed algorithm is enhanced by a higher-dimensional mapping of the disorder\npattern and using two neural networks, each properly trained for the given\ntask. The designed method, being computationally more efficient than the\ngradient-descent optimization, can be applicable to identify and control\nvarious noisy quantum systems on a heuristic basis.", "category": "cond-mat_dis-nn" }, { "text": "Spin relaxation in a Rashba semiconductor in an electric field: The impact of an external electric field on the spin relaxation in a\ndisordered two-dimensional electron system is studied within the framework of a\nfield-theoretical formulation. Generalized Bloch-equations for the diffusion\nand the decay of an initial magnetization are obtained. The equations are\napplied to the investigation of spin relaxation processes in an electric field.", "category": "cond-mat_dis-nn" }, { "text": "Analytical solutions for Ising models on high dimensional lattices: We use an m-vicinity method to examine Ising models on hypercube lattices of\nhigh dimensions d>=3. This method is applicable for both short-range and\nlong-range interactions. We introduce a small parameter, which determines\nwhether the method can be used when calculating the free energy. When we\naccount for interaction with the nearest neighbors only, the value of this\nparameter depends on the dimension of the lattice d. We obtain an expression\nfor the critical temperature in terms of the interaction constants that is in a\ngood agreement with results of computer simulations. For d=5, 6, 7, our\ntheoretical estimates match the experiments both qualitatively and\nquantitatively. For d=3, 4, our method is sufficiently accurate for calculation\nof the critical temperatures, however, it predicts a finite jump of the heat\ncapacity at the critical point. In the case of the three-dimensional lattice\n(d=3), this contradicts to the commonly accepted ideas of the type of the\nsingularity at the critical point. For the four-dimensional lattice (d = 4) the\ncharacter of the singularity is under current discussion. For the dimensions\nd=1, 2 the m-vicinity method is not applicable.", "category": "cond-mat_dis-nn" }, { "text": "A new view of the Lindemann criterion: The Lindemann criterion is reformulated in terms of the average shear modulus\n$G_c$ of the melting crystal, indicating a critical melting shear strain which\nis necessary to form the many different inherent states of the liquid. In glass\nformers with covalent bonds, one has to distinguish between soft and hard\ndegrees of freedom to reach agreement. The temperature dependence of the\npicosecond mean square displacements of liquid and crystal shows that there are\ntwo separate contributions to the divergence of the viscosity with decreasing\ntemperature: the anharmonic increase of the shear modulus and a diverging\ncorrelation length .", "category": "cond-mat_dis-nn" }, { "text": "Generalized Lyapunov Exponent and Transmission Statistics in\n One-dimensional Gaussian Correlated Potentials: Distribution of the transmission coefficient T of a long system with a\ncorrelated Gaussian disorder is studied analytically and numerically in terms\nof the generalized Lyapunov exponent (LE) and the cumulants of lnT. The effect\nof the disorder correlations on these quantities is considered in weak,\nmoderate and strong disorder for different models of correlation. Scaling\nrelations between the cumulants of lnT are obtained. The cumulants are treated\nanalytically within the semiclassical approximation in strong disorder, and\nnumerically for an arbitrary strength of the disorder. A small correlation\nscale approximation is developed for calculation of the generalized LE in a\ngeneral correlated disorder. An essential effect of the disorder correlations\non the transmission statistics is found. In particular, obtained relations\nbetween the cumulants and between them and the generalized LE show that, beyond\nweak disorder, transmission fluctuations and deviation of their distribution\nfrom the log-normal form (in a long but finite system) are greatly enhanced due\nto the disorder correlations. Parametric dependence of these effects upon the\ncorrelation scale is presented.", "category": "cond-mat_dis-nn" }, { "text": "Many-body localization in a fragmented Hilbert space: We study many-body localization (MBL) in a pair-hopping model exhibiting\nstrong fragmentation of the Hilbert space. We show that several Krylov\nsubspaces have both ergodic statistics in the thermodynamic limit and a\ndimension that scales much slower than the full Hilbert space, but still\nexponentially. Such a property allows us to study the MBL phase transition in\nsystems including more than $50$ spins. The different Krylov spaces that we\nconsider show clear signatures of a many-body localization transition, both in\nthe Kullback-Leibler divergence of the distribution of their level spacing\nratio and their entanglement properties. But they also present distinct\nscalings with system size. Depending on the subspace, the critical disorder\nstrength can be nearly independent of the system size or conversely show an\napproximately linear increase with the number of spins.", "category": "cond-mat_dis-nn" }, { "text": "New universal conductance fluctuation of mesoscopic systems in the\n crossover regime from metal to insulator: We report a theoretical investigation on conductance fluctuation of\nmesoscopic systems. Extensive numerical simulations on quasi-one dimensional,\ntwo dimensional, and quantum dot systems with different symmetries (COE, CUE,\nand CSE) indicate that the conductance fluctuation can reach a new universal\nvalue in the crossover regime for systems with CUE and CSE symmetries. The\nconductance fluctuation and higher order moments vs average conductance were\nfound to be universal functions from diffusive to localized regimes that depend\nonly on the dimensionality and symmetry. The numerical solution of DMPK\nequation agrees with our result in quasi-one dimension. Our numerical results\nin two dimensions suggest that this new universal conductance fluctuation is\nrelated to the metal-insulator transition.", "category": "cond-mat_dis-nn" }, { "text": "Random maps and attractors in random Boolean networks: Despite their apparent simplicity, random Boolean networks display a rich\nvariety of dynamical behaviors. Much work has been focused on the properties\nand abundance of attractors. The topologies of random Boolean networks with one\ninput per node can be seen as graphs of random maps. We introduce an approach\nto investigating random maps and finding analytical results for attractors in\nrandom Boolean networks with the corresponding topology. Approximating some\nother non-chaotic networks to be of this class, we apply the analytic results\nto them. For this approximation, we observe a strikingly good agreement on the\nnumbers of attractors of various lengths. We also investigate observables\nrelated to the average number of attractors in relation to the typical number\nof attractors. Here, we find strong differences that highlight the difficulties\nin making direct comparisons between random Boolean networks and real systems.\nFurthermore, we demonstrate the power of our approach by deriving some results\nfor random maps. These results include the distribution of the number of\ncomponents in random maps, along with asymptotic expansions for cumulants up to\nthe 4th order.", "category": "cond-mat_dis-nn" }, { "text": "Network Structure, Topology and Dynamics in Generalized Models of\n Synchronization: We explore the interplay of network structure, topology, and dynamic\ninteractions between nodes using the paradigm of distributed synchronization in\na network of coupled oscillators. As the network evolves to a global steady\nstate, interconnected oscillators synchronize in stages, revealing network's\nunderlying community structure. Traditional models of synchronization assume\nthat interactions between nodes are mediated by a conservative process, such as\ndiffusion. However, social and biological processes are often non-conservative.\nWe propose a new model of synchronization in a network of oscillators coupled\nvia non-conservative processes. We study dynamics of synchronization of a\nsynthetic and real-world networks and show that different synchronization\nmodels reveal different structures within the same network.", "category": "cond-mat_dis-nn" }, { "text": "Duality in finite-dimensional spin glasses: We present an analysis leading to a conjecture on the exact location of the\nmulticritical point in the phase diagram of spin glasses in finite dimensions.\nThe conjecture, in satisfactory agreement with a number of numerical results,\nwas previously derived using an ansatz emerging from duality and the replica\nmethod. In the present paper we carefully examine the ansatz and reduce it to a\nhypothesis on analyticity of a function appearing in the duality relation. Thus\nthe problem is now clearer than before from a mathematical point of view: The\nansatz, somewhat arbitrarily introduced previously, has now been shown to be\nclosely related to the analyticity of a well-defined function.", "category": "cond-mat_dis-nn" }, { "text": "Erratum: Small-world networks: Evidence for a crossover picture: We correct the value of the exponent \\tau.", "category": "cond-mat_dis-nn" }, { "text": "Solvable Models of Supercooled Liquids in Three Dimensions: We introduce a supercooled liquid model and obtain parameter-free\nquantitative predictions that are in excellent agreement with numerical\nsimulations, notably in the hard low-temperature region characterized by strong\ndeviations from Mode-Coupling-Theory behavior. The model is the\nFredrickson-Andersen Kinetically-Constrained-Model on the three-dimensional\n$M$-layer lattice. The agreement has implications beyond the specific model\nconsidered because the theory is potentially valid for many more systems,\nincluding realistic models and actual supercooled liquids.", "category": "cond-mat_dis-nn" }, { "text": "On the ground states of the Bernasconi model: The ground states of the Bernasconi model are binary +1/-1 sequences of\nlength N with low autocorrelations. We introduce the notion of perfect\nsequences, binary sequences with one-valued off-peak correlations of minimum\namount. If they exist, they are ground states. Using results from the\nmathematical theory of cyclic difference sets, we specify all values of N for\nwhich perfect sequences do exist and how to construct them. For other values of\nN, we investigate almost perfect sequences, i.e. sequences with two-valued\noff-peak correlations of minimum amount. Numerical and analytical results\nsupport the conjecture that almost perfect sequences do exist for all values of\nN, but that they are not always ground states. We present a construction for\nlow-energy configurations that works if N is the product of two odd primes.", "category": "cond-mat_dis-nn" }, { "text": "Hyperuniform vortex patterns at the surface of type-II superconductors: A many-particle system must posses long-range interactions in order to be\nhyperuniform at thermal equilibrium. Hydrodynamic arguments and numerical\nsimulations show, nevertheless, that a three-dimensional elastic-line array\nwith short-ranged repulsive interactions, such as vortex matter in a type-II\nsuperconductor, forms at equilibrium a class-II hyperuniform two-dimensional\npoint pattern for any constant-$z$ cross section. In this case, density\nfluctuations vanish isotropically as $\\sim q^{\\alpha}$ at small wave-vectors\n$q$, with $\\alpha=1$. This prediction includes the solid and liquid vortex\nphases in the ideal clean case, and the liquid in presence of weak uncorrelated\ndisorder. We also show that the three-dimensional Bragg glass phase is\nmarginally hyperuniform, while the Bose glass and the liquid phase with\ncorrelated disorder are expected to be non-hyperuniform at equilibrium.\nFurthermore, we compare these predictions with experimental results on the\nlarge-wavelength vortex density fluctuations of magnetically decorated vortex\nstructures nucleated in pristine, electron-irradiated and heavy-ion irradiated\nsuperconducting BiSCCO samples in the mixed state. For most cases we find\nhyperuniform two-dimensional point patterns at the superconductor surface with\nan effective exponent $\\alpha_{\\text{eff}} \\approx 1$. We interpret these\nresults in terms of a large-scale memory of the high-temperature line-liquid\nphase retained in the glassy dynamics when field-cooling the vortex structures\ninto the solid phase. We also discuss the crossovers expected from the\ndispersivity of the elastic constants at intermediate length-scales, and the\nlack of hyperuniformity in the $x\\,-y$ plane for lengths $q^{-1}$ larger than\nthe sample thickness due to finite-size effects in the $z$-direction.", "category": "cond-mat_dis-nn" }, { "text": "Relationship between non-exponentiality of relaxation and relaxation\n time at the glass transition: By analyzing the experimental data for various glass-forming liquids and\npolymers, we find that non-exponentiality $\\beta$ and the relaxation time\n$\\tau$ are uniquely related: $\\log(\\tau)$ is an approximately linear function\nof $1/\\beta$, followed by a crossover to a higher linear slope. We rationalize\nthe observed relationship using a recently developed approach, in which the\nproblem of the glass transition is discussed as the elasticity problem.", "category": "cond-mat_dis-nn" }, { "text": "High values of disorder-generated multifractals and logarithmically\n correlated processes: In the introductory section of the article we give a brief account of recent\ninsights into statistics of high and extreme values of disorder-generated\nmultifractals following a recent work by the first author with P. Le Doussal\nand A. Rosso (FLR) employing a close relation between multifractality and\nlogarithmically correlated random fields. We then substantiate some aspects of\nthe FLR approach analytically for multifractal eigenvectors in the\nRuijsenaars-Schneider ensemble (RSE) of random matrices introduced by E.\nBogomolny and the second author by providing an ab initio calculation that\nreveals hidden logarithmic correlations at the background of the\ndisorder-generated multifractality. In the rest we investigate numerically a\nfew representative models of that class, including the study of the highest\ncomponent of multifractal eigenvectors in the Ruijsenaars-Schneider ensemble.", "category": "cond-mat_dis-nn" }, { "text": "On Properties of Boundaries and Electron Conductivity in Mesoscopic\n Polycrystalline Silicon Films for Memory Devices: We present the results of molecular dynamics modeling on the structural\nproperties of grain boundaries (GB) in thin polycrystalline films. The\ntransition from crystalline boundaries with low mismatch angle to amorphous\nboundaries is investigated. It is shown that the structures of the GBs satisfy\na thermodynamical criterion. The potential energy of silicon atoms is closely\nrelated with a geometrical quantity -- tetragonality of their coordination with\ntheir nearest neighbors. A crossover of the length of localization is observed.\nTo analyze the crossover of the length of localization of the single-electron\nstates and properties of conductance of the thin polycrystalline film at low\ntemperature, we use a two-dimensional Anderson localization model, with the\nrandom one-site electron charging energy for a single grain (dot), random\nnon-diagonal matrix elements, and random number of connections between the\nneighboring grains. The results on the crossover behavior of localization\nlength of the single-electron states and characteristic properties of\nconductance are presented in the region of parameters where the transition from\nan insulator to a conductor regimes takes place.", "category": "cond-mat_dis-nn" }, { "text": "On the polyamorphism of fullerite-based orientational glasses: The dilatometric investigation in the temperature range of 2-28K shows that a\nfirst-order polyamorphous transition occurs in the orientational glasses based\non C60 doped with H2, D2 and Xe. A polyamorphous transition was also detected\nin C60 doped with Kr and He. It is observed that the hysteresis of thermal\nexpansion caused by the polyamorphous transition (and, hence, the transition\ntemperature) is essentially dependent on the type of doping gas. Both positive\nand negative contributions to the thermal expansion were observed in the low\ntemperature phase of the glasses. The relaxation time of the negative\ncontribution occurs to be much longer than that of the positive contribution.\nThe positive contribution is found to be due to phonon and libron modes, whilst\nthe negative contribution is attributed to tunneling states of the C60\nmolecules. The characteristic time of the phase transformation from the low-T\nphase to the high-T phase has been found for the C60-H2 system at 12K. A\ntheoretical model is proposed to interpret these observed phenomena. The\ntheoretical model proposed, includes a consideration of the nature of\npolyamorphism in glasses, as well as the thermodynamics and kinetics of the\ntransition. A model of non-interacting tunneling states is used to explain the\nnegative contribution to the thermal expansion. The experimental data obtained\nis considered within the framework of the theoretical model. From the\ntheoretical model the order of magnitude of the polyamorphous transition\ntemperature has been estimated. It is found that the late stage of the\npolyamorphous transformation is described well by the Kolmogorov law with an\nexponent of n=1. At this stage of the transformation, the two-dimensional phase\nboundary moves along the normal, and the nucleation is not important.", "category": "cond-mat_dis-nn" }, { "text": "Cracks in random brittle solids: From fiber bundles to continuum\n mechanics: Statistical models are essential to get a better understanding of the role of\ndisorder in brittle disordered solids. Fiber bundle models play a special role\nas a paradigm, with a very good balance of simplicity and non-trivial effects.\nWe introduce here a variant of the fiber bundle model where the load is\ntransferred among the fibers through a very compliant membrane. This Soft\nMembrane fiber bundle mode reduces to the classical Local Load Sharing fiber\nbundle model in 1D. Highlighting the continuum limit of the model allows to\ncompute an equivalent toughness for the fiber bundle and hence discuss\nnucleation of a critical defect. The computation of the toughness allows for\ndrawing a simple connection with crack front propagation (depinning) models.", "category": "cond-mat_dis-nn" }, { "text": "Resonance width distribution for high-dimensional random media: We study the distribution of resonance widths P(G) for three-dimensional (3D)\nrandom scattering media and analyze how it changes as a function of the\nrandomness strength. We are able to identify in P(G) the system-inherent\nfingerprints of the metallic, localized, and critical regimes. Based on the\nproperties of resonance widths, we also suggest a new criterion for determining\nand analyzing the metal-insulator transition. Our theoretical predictions are\nverified numerically for the prototypical 3D tight-binding Anderson model.", "category": "cond-mat_dis-nn" }, { "text": "Activity patterns on random scale-free networks: Global dynamics arising\n from local majority rules: Activity or spin patterns on random scale-free network are studied by mean\nfield analysis and computer simulations. These activity patterns evolve in time\naccording to local majority-rule dynamics which is implemented using (i)\nparallel or synchronous updating and (ii) random sequential or asynchronous\nupdating. Our mean-field calculations predict that the relaxation processes of\ndisordered activity patterns become much more efficient as the scaling exponent\n$\\gamma$ of the scale-free degree distribution changes from $\\gamma >5/2$ to\n$\\gamma < 5/2$. For $\\gamma > 5/2$, the corresponding decay times increase as\n$\\ln(N)$ with increasing network size $N$ whereas they are independent of $N$\nfor $\\gamma < 5/2$. In order to check these mean field predictions, extensive\nsimulations of the pattern dynamics have been performed using two different\nensembles of random scale-free networks: (A) multi-networks as generated by the\nconfiguration method, which typically leads to many self-connections and\nmultiple edges, and (B) simple-networks without self-connections and multiple\nedges.", "category": "cond-mat_dis-nn" }, { "text": "Non-Arrhenius Behavior of Secondary Relaxation in Supercooled Liquids: Dielectric relaxation spectroscopy (1 Hz - 20 GHz) has been performed on\nsupercooled glass-formers from the temperature of glass transition (T_g) up to\nthat of melting. Precise measurements particularly in the frequencies of\nMHz-order have revealed that the temperature dependences of secondary\nbeta-relaxation times deviate from the Arrhenius relation in well above T_g.\nConsequently, our results indicate that the beta-process merges into the\nprimary alpha-mode around the melting temperature, and not at the dynamical\ntransition point T which is approximately equal to 1.2 T_g.", "category": "cond-mat_dis-nn" }, { "text": "Bond dilution in the 3D Ising model: a Monte Carlo study: We study by Monte Carlo simulations the influence of bond dilution on the\nthree-dimensional Ising model. This paradigmatic model in its pure version\ndisplays a second-order phase transition with a positive specific heat critical\nexponent $\\alpha$. According to the Harris criterion disorder should hence lead\nto a new fixed point characterized by new critical exponents. We have\ndetermined the phase diagram of the diluted model, between the pure model limit\nand the percolation threshold. For the estimation of critical exponents, we\nhave first performed a finite-size scaling study, where we concentrated on\nthree different dilutions. We emphasize in this work the great influence of the\ncross-over phenomena between the pure, disorder and percolation fixed points\nwhich lead to effective critical exponents dependent on the concentration. In a\nsecond set of simulations, the temperature behaviour of physical quantities has\nbeen studied in order to characterize the disorder fixed point more accurately.\nIn particular this allowed us to estimate ratios of some critical amplitudes.\nIn accord with previous observations for other models this provides stronger\nevidence for the existence of the disorder fixed point since the amplitude\nratios are more sensitive to the universality class than the critical\nexponents. Moreover, the question of non-self-averaging at the disorder fixed\npoint is investigated and compared with recent results for the bond-diluted\n$q=4$ Potts model. Overall our numerical results provide evidence that, as\nexpected on theoretical grounds, the critical behaviour of the bond-diluted\nmodel is governed by the same universality class as the site-diluted model.", "category": "cond-mat_dis-nn" }, { "text": "Analytical representations for relaxation functions of glasses: Analytical representations in the time and frequency domains are derived for\nthe most frequently used phenomenological fit functions for non-Debye\nrelaxation processes. In the time domain the relaxation functions corresponding\nto the complex frequency dependent Cole-Cole, Cole-Davidson and\nHavriliak-Negami susceptibilities are also represented in terms of\n$H$-functions. In the frequency domain the complex frequency dependent\nsusceptibility function corresponding to the time dependent stretched\nexponential relaxation function is given in terms of $H$-functions. The new\nrepresentations are useful for fitting to experiment.", "category": "cond-mat_dis-nn" }, { "text": "Crossover from Scale-Free to Spatial Networks: In many networks such as transportation or communication networks, distance\nis certainly a relevant parameter. In addition, real-world examples suggest\nthat when long-range links are existing, they usually connect to hubs-the well\nconnected nodes. We analyze a simple model which combine both these\ningredients--preferential attachment and distance selection characterized by a\ntypical finite `interaction range'. We study the crossover from the scale-free\nto the `spatial' network as the interaction range decreases and we propose\nscaling forms for different quantities describing the network. In particular,\nwhen the distance effect is important (i) the connectivity distribution has a\ncut-off depending on the node density, (ii) the clustering coefficient is very\nhigh, and (iii) we observe a positive maximum in the degree correlation\n(assortativity) which numerical value is in agreement with empirical\nmeasurements. Finally, we show that if the number of nodes is fixed, the\noptimal network which minimizes both the total length and the diameter lies in\nbetween the scale-free and spatial networks. This phenomenon could play an\nimportant role in the formation of networks and could be an explanation for the\nhigh clustering and the positive assortativity which are non trivial features\nobserved in many real-world examples.", "category": "cond-mat_dis-nn" }, { "text": "Managing catastrophic changes in a collective: We address the important practical issue of understanding, predicting and\neventually controlling catastrophic endogenous changes in a collective. Such\nlarge internal changes arise as macroscopic manifestations of the microscopic\ndynamics, and their presence can be regarded as one of the defining features of\nan evolving complex system. We consider the specific case of a multi-agent\nsystem related to the El Farol bar model, and show explicitly how the\ninformation concerning such large macroscopic changes becomes encoded in the\nmicroscopic dynamics. Our findings suggest that these large endogenous changes\ncan be avoided either by pre-design of the collective machinery itself, or in\nthe post-design stage via continual monitoring and occasional `vaccinations'.", "category": "cond-mat_dis-nn" }, { "text": "Statistical Mechanics of Online Learning of Drifting Concepts : A\n Variational Approach: We review the application of Statistical Mechanics methods to the study of\nonline learning of a drifting concept in the limit of large systems. The model\nwhere a feed-forward network learns from examples generated by a time dependent\nteacher of the same architecture is analyzed. The best possible generalization\nability is determined exactly, through the use of a variational method. The\nconstructive variational method also suggests a learning algorithm. It depends,\nhowever, on some unavailable quantities, such as the present performance of the\nstudent. The construction of estimators for these quantities permits the\nimplementation of a very effective, highly adaptive algorithm. Several other\nalgorithms are also studied for comparison with the optimal bound and the\nadaptive algorithm, for different types of time evolution of the rule.", "category": "cond-mat_dis-nn" }, { "text": "Disorder driven itinerant quantum criticality of three dimensional\n massless Dirac fermions: Progress in the understanding of quantum critical properties of itinerant\nelectrons has been hindered by the lack of effective models which are amenable\nto controlled analytical and numerically exact calculations. Here we establish\nthat the disorder driven semimetal to metal quantum phase transition of three\ndimensional massless Dirac fermions could serve as a paradigmatic toy model for\nstudying itinerant quantum criticality, which is solved in this work by exact\nnumerical and approximate field theoretic calculations. As a result, we\nestablish the robust existence of a non-Gaussian universality class, and also\nconstruct the relevant low energy effective field theory that could guide the\nunderstanding of quantum critical scaling for many strange metals. Using the\nkernel polynomial method (KPM), we provide numerical results for the calculated\ndynamical exponent ($z$) and correlation length exponent ($\\nu$) for the\ndisorder-driven semimetal (SM) to diffusive metal (DM) quantum phase transition\nat the Dirac point for several types of disorder, establishing its universal\nnature and obtaining the numerical scaling functions in agreement with our\nfield theoretical analysis.", "category": "cond-mat_dis-nn" }, { "text": "Distribution of zeros of the S-matrix of chaotic cavities with localized\n losses and Coherent Perfect Absorption: non-perturbative results: We employ the Random Matrix Theory framework to calculate the density of\nzeroes of an $M$-channel scattering matrix describing a chaotic cavity with a\nsingle localized absorber embedded in it. Our approach extends beyond the\nweak-coupling limit of the cavity with the channels and applies for any\nabsorption strength. Importantly it provides an insight for the optimal amount\nof loss needed to realize a chaotic coherent perfect absorbing (CPA) trap. Our\npredictions are tested against simulations for two types of traps: a complex\nnetwork of resonators and quantum graphs.", "category": "cond-mat_dis-nn" }, { "text": "Intermittent dynamics and logarithmic domain growth during the spinodal\n decomposition of a glass-forming liquid: We use large-scale molecular dynamics simulations of a simple glass-forming\nsystem to investigate how its liquid-gas phase separation kinetics depends on\ntemperature. A shallow quench leads to a fully demixed liquid-gas system\nwhereas a deep quench makes the dense phase undergo a glass transition and\nbecome an amorphous solid. This glass has a gel-like bicontinuous structure\nthat evolves very slowly with time and becomes fully arrested in the limit\nwhere thermal fluctuations become negligible. We show that the phase separation\nkinetics changes qualitatively with temperature, the microscopic dynamics\nevolving from a surface tension-driven diffusive motion at high temperature to\na strongly intermittent, heterogeneous and thermally activated dynamics at low\ntemperature, with a logarithmically slow growth of the typical domain size.\nThese results shed light on recent experimental observations of various porous\nmaterials produced by arrested spinodal decomposition, such as nonequilibrium\ncolloidal gels and bicontinuous polymeric structures, and they elucidate the\nmicroscopic mechanisms underlying a specific class of viscoelastic phase\nseparation.", "category": "cond-mat_dis-nn" }, { "text": "The Cavity Approach to Noisy Learning in Nonlinear Perceptrons: We analyze the learning of noisy teacher-generated examples by nonlinear and\ndifferentiable student perceptrons using the cavity method. The generic\nactivation of an example is a function of the cavity activation of the example,\nwhich is its activation in the perceptron that learns without the example. Mean\nfield equations for the macroscopic parameters and the stability condition\nyield results consistent with the replica method. When a single value of the\ncavity activation maps to multiple values of the generic activation, there is a\ncompetition in learning strategy between preferentially learning an example and\nsacrificing it in favor of the background adjustment. We find parameter regimes\nin which examples are learned preferentially or sacrificially, leading to a gap\nin the activation distribution. Full phase diagrams of this complex system are\npresented, and the theory predicts the existence of a phase transition from\npoor to good generalization states in the system. Simulation results confirm\nthe theoretical predictions.", "category": "cond-mat_dis-nn" }, { "text": "Machine learning assisted measurement of local topological invariants: The continuous effort towards topological quantum devices calls for an\nefficient and non-invasive method to assess the conformity of components in\ndifferent topological phases. Here, we show that machine learning paves the way\ntowards non-invasive topological quality control. To do so, we use a local\ntopological marker, able to discriminate between topological phases of\none-dimensional wires. The direct observation of this marker in solid state\nsystems is challenging, but we show that an artificial neural network can learn\nto approximate it from the experimentally accessible local density of states.\nOur method distinguishes different non-trivial phases, even for systems where\ndirect transport measurements are not available and for composite systems. This\nnew approach could find significant use in experiments, ranging from the study\nof novel topological materials to high-throughput automated material design.", "category": "cond-mat_dis-nn" }, { "text": "Structural Signatures for Thermodynamic Stability in Vitreous Silica:\n Insight from Machine Learning and Molecular Dynamics Simulations: The structure-thermodynamic stability relationship in vitreous silica is\ninvestigated using machine learning and a library of 24,157 inherent structures\ngenerated from melt-quenching and replica exchange molecular dynamics\nsimulations. We find the thermodynamic stability, i.e., enthalpy of the\ninherent structure ($e_{\\mathrm{IS}}$), can be accurately predicted by both\nlinear and nonlinear machine learning models from numeric structural\ndescriptors commonly used to characterize disordered structures. We find\nshort-range features become less indicative of thermodynamic stability below\nthe fragile-to-strong transition. On the other hand, medium-range features,\nespecially those between 2.8-~6 $\\unicode{x212B}$;, show consistent\ncorrelations with $e_{\\mathrm{IS}}$ across the liquid and glass regions, and\nare found to be the most critical to stability prediction among features from\ndifferent length scales. Based on the machine learning models, a set of five\nstructural features that are the most predictive of the silica glass stability\nis identified.", "category": "cond-mat_dis-nn" }, { "text": "Origin of the unusual dependence of Raman D band on excitation\n wavelength in graphite-like materials: We have revisited the still unresolved puzzle of the dispersion of the Raman\ndisordered-induced D band as a function of laser excitation photon energy E$_L$\nin graphite-like materials. We propose that the D-mode is a combination of an\noptic phonon at the K-point in the Brillioun zone and an acoustic phonon whose\nmomentum is determined uniquely by the double resonance condition. The fit of\nthe experimental data with the double-resonance model yields the reduced\neffective mass of 0.025m$_{e}$ for the electron-hole pairs corresponding to the\nA$_{2}$ transition, in agreement with other experiments. The model can also\nexplain the difference between $\\omega_S$ and $\\omega_{AS}$ for D and\nD$^{\\star}$ modes, and predicts its dependence on the Raman excitation\nfrequency.", "category": "cond-mat_dis-nn" }, { "text": "Infrared-Induced Sluggish Dynamics in the GeSbTe Electron Glass: The electron-glass dynamics of Anderson-localized GeSbTe films is\ndramatically slowed-down following a brief infrared illumination that increases\nthe system carrier-concentration (and thus its conductance). These results\ndemonstrate that the dynamics exhibited by electron-glasses is more sensitive\nto carrier-concentration than to disorder. In turn, this seems to imply that\nmany-body effects such as the Orthogonality Catastrophe must play a role in the\nsluggish dynamics observed in the intrinsic electron-glasses.", "category": "cond-mat_dis-nn" }, { "text": "Inducing periodicity in lattices of chaotic maps with advection: We investigate a lattice of coupled logistic maps where, in addition to the\nusual diffusive coupling, an advection term parameterized by an asymmetry in\nthe coupling is introduced. The advection term induces periodic behavior on a\nsignificant number of non-periodic solutions of the purely diffusive case. Our\nresults are based on the characteristic exponents for such systems, namely the\nmean Lyapunov exponent and the co-moving Lyapunov exponent. In addition, we\nstudy how to deal with more complex phenomena in which the advective velocity\nmay vary from site to site. In particular, we observe wave-like pulses to\nappear and disappear intermittently whenever the advection is spatially\ninhomogeneous.", "category": "cond-mat_dis-nn" }, { "text": "Statistical Mechanics of Dictionary Learning: Finding a basis matrix (dictionary) by which objective signals are\nrepresented sparsely is of major relevance in various scientific and\ntechnological fields. We consider a problem to learn a dictionary from a set of\ntraining signals. We employ techniques of statistical mechanics of disordered\nsystems to evaluate the size of the training set necessary to typically succeed\nin the dictionary learning. The results indicate that the necessary size is\nmuch smaller than previously estimated, which theoretically supports and/or\nencourages the use of dictionary learning in practical situations.", "category": "cond-mat_dis-nn" }, { "text": "Anomalously Strong Nonlinearity of Unswept Quartz Acoustic Cavities at\n Liquid Helium Temperatures: We demonstrate a variety of nonlinear phenomena at extremely low powers in\ncryogenic acoustic cavities fabricated from quartz material, which have not\nundergone any electrodiffusion processes. Nonlinear phenomena observed include\nlineshape discontinuities, power response discontinuities, quadrature\noscillations and self-induced transparency. These phenomena are attributed to\nnonlinear dissipation through a large number of randomly distributed heavy\ntrapped ions, which would normally be removed by electrodiffusion. A simple\nmean-field model predicts most of the observed phenomena. In contrast to\nDuffing-like systems, this system shows an unusual mechanism of nonlinearity,\nwhich is not related to crystal anharmonisity.", "category": "cond-mat_dis-nn" }, { "text": "Avalanches in Tip-Driven Interfaces in Random Media: We analyse by numerical simulations and scaling arguments the avalanche\nstatistics of 1-dimensional elastic interfaces in random media driven at a\nsingle point. Both global and local avalanche sizes are power-law distributed,\nwith universal exponents given by the depinning roughness exponent $\\zeta$ and\nthe interface dimension $d$, and distinct from their values in the uniformly\ndriven case. A crossover appears between uniformly driven behaviour for small\navalanches, and point driven behaviour for large avalanches. The scale of the\ncrossover is controlled by the ratio between the stiffness of the pulling\nspring and the elasticity of the interface; it is visible both in the global\nand local avalanche-size distributions, as in the average spatial avalanche\nshape. Our results are relevant to model experiments involving locally driven\nelastic manifolds at low temperatures, such as magnetic domain walls or vortex\nlines in superconductors.", "category": "cond-mat_dis-nn" }, { "text": "The Leontovich boundary conditions and calculation of effective\n impedance of inhomogeneous metal: We bring forward rather simple algorithm allowing us to calculate the\neffective impedance of inhomogeneous metals in the frequency region where the\nlocal Leontovich (the impedance) boundary conditions are justified. The\ninhomogeneity is due to the properties of the metal or/and the surface\nroughness. Our results are nonperturbative ones with respect to the\ninhomogeneity amplitude. They are based on the recently obtained exact result\nfor the effective impedance of inhomogeneous metals with flat surfaces.\nOne-dimension surfaces inhomogeneities are examined. Particular attention is\npaid to the influence of generated evanescent waves on the reflection\ncharacteristics. We show that if the surface roughness is rather strong, the\nelement of the effective impedance tensor relating to the p- polarization state\nis much greater than the input local impedance. As examples, we calculate: i)\nthe effective impedance for a flat surface with strongly nonhomogeneous\nperiodic strip-like local impedance; ii) the effective impedance associated\nwith one-dimensional lamellar grating. For the problem (i) we also present\nequations for the forth lines of the Pointing vector in the vicinity of the\nsurface.", "category": "cond-mat_dis-nn" }, { "text": "StrainTensorNet: Predicting crystal structure elastic properties using\n SE(3)-equivariant graph neural networks: Accurately predicting the elastic properties of crystalline solids is vital\nfor computational materials science. However, traditional atomistic scale ab\ninitio approaches are computationally intensive, especially for studying\ncomplex materials with a large number of atoms in a unit cell. We introduce a\nnovel data-driven approach to efficiently predict the elastic properties of\ncrystal structures using SE(3)-equivariant graph neural networks (GNNs). This\napproach yields important scalar elastic moduli with the accuracy comparable to\nrecent data-driven studies. Importantly, our symmetry-aware GNNs model also\nenables the prediction of the strain energy density (SED) and the associated\nelastic constants, the fundamental tensorial quantities that are significantly\ninfluenced by a material's crystallographic group. The model consistently\ndistinguishes independent elements of SED tensors, in accordance with the\nsymmetry of the crystal structures. Finally, our deep learning model possesses\nmeaningful latent features, offering an interpretable prediction of the elastic\nproperties.", "category": "cond-mat_dis-nn" }, { "text": "Monte Carlo studies of the chiral and spin orderings of the\n three-dimensional Heisenberg spin glass: The nature of the ordering of the three-dimensional isotropic Heisenberg spin\nglass with nearest-neighbor random Gaussian coupling is studied by extensive\nMonte Carlo simulations. Several independent physical quantities are measured\nboth for the spin and for the chirality, including the correlation-length\nratio, the Binder ratio, the glass order parameter, the overlap distribution\nfunction and the non-self-averageness parameter. By controlling the effect of\nthe correction-to-scaling, we have obtained a numerical evidence for the\noccurrence of successive chiral-glass and spin-glass transitions at nonzero\ntemperatures, T_{CG} > T_{SG} > 0. Hence, the spin and the chirality are\ndecoupled in the ordering of the model. The chiral-glass exponents are\nestimated to be \\nu_{CG}=1.4+-0.2 and \\eta_{CG}=0.6+-0.2, indicating that the\nchiral-glass transition lies in a universality class different from that of the\nIsing spin glass. The possibility that the spin and chiral sectors undergo a\nsimultaneous Kosterlitz-Thouless-type transition is ruled out. The chiral-glass\nstate turns out to be non-self-averaging, possibly accompanying a one-step-like\npeculiar replica-symmetry breaking. Implications to the chirality scenario of\nexperimental spin-glass transitions are discussed.", "category": "cond-mat_dis-nn" }, { "text": "Ground-State and Domain-Wall Energies in the Spin-Glass Region of the 2D\n $\\pm J$ Random-Bond Ising Model: The statistics of the ground-state and domain-wall energies for the\ntwo-dimensional random-bond Ising model on square lattices with independent,\nidentically distributed bonds of probability $p$ of $J_{ij}= -1$ and $(1-p)$ of\n$J_{ij}= +1$ are studied. We are able to consider large samples of up to\n$320^2$ spins by using sophisticated matching algorithms. We study $L \\times L$\nsystems, but we also consider $L \\times M$ samples, for different aspect ratios\n$R = L / M$. We find that the scaling behavior of the ground-state energy and\nits sample-to-sample fluctuations inside the spin-glass region ($p_c \\le p \\le\n1 - p_c$) are characterized by simple scaling functions. In particular, the\nfluctuations exhibit a cusp-like singularity at $p_c$. Inside the spin-glass\nregion the average domain-wall energy converges to a finite nonzero value as\nthe sample size becomes infinite, holding $R$ fixed. Here, large finite-size\neffects are visible, which can be explained for all $p$ by a single exponent\n$\\omega\\approx 2/3$, provided higher-order corrections to scaling are included.\nFinally, we confirm the validity of aspect-ratio scaling for $R \\to 0$: the\ndistribution of the domain-wall energies converges to a Gaussian for $R \\to 0$,\nalthough the domain walls of neighboring subsystems of size $L \\times L$ are\nnot independent.", "category": "cond-mat_dis-nn" }, { "text": "Phase diagram of disordered fermion model on two-dimensional square\n lattice with $\u03c0$-flux: A fermion model with random on-site potential defined on a two-dimensional\nsquare lattice with $\\pi$-flux is studied. The continuum limit of the model\nnear the zero energy yields Dirac fermions with random potentials specified by\nfour independent coupling constants. The basic symmetry of the model is\ntime-reversal invariance. Moreover, it turns out that the model has enhanced\n(chiral) symmetry on several surfaces in the four-dimensional space of the\ncoupling constants. It is shown that one of the surfaces with chiral symmetry\nhas Sp(n)$\\times$Sp(n) symmety whereas others have U(2n) symmetry, both of\nwhich are broken to Sp(n), and the fluctuation around a saddle point is\ndescribed, respectively, by Sp($n)_2$ WZW model and U(2n)/Sp(n) nonlinear sigma\nmodel. Based on these results, we propose a phase diagram of the model.", "category": "cond-mat_dis-nn" }, { "text": "Boundary-driven Lindblad dynamics of random quantum spin chains : strong\n disorder approach for the relaxation, the steady state and the current: The Lindblad dynamics of the XX quantum chain with large random fields $h_j$\n(the couplings $J_j$ can be either uniform or random) is considered for\nboundary-magnetization-drivings acting on the two end-spins. Since each\nboundary-reservoir tends to impose its own magnetization, we first study the\nrelaxation spectrum in the presence of a single reservoir as a function of the\nsystem size via some boundary-strong-disorder renormalization approach. The\nnon-equilibrium-steady-state in the presence of two reservoirs can be then\nanalyzed from the effective renormalized Linbladians associated to the two\nreservoirs. The magnetization is found to follow a step profile, as found\npreviously in other localized chains. The strong disorder approach allows to\ncompute explicitly the location of the step of the magnetization profile and\nthe corresponding magnetization-current for each disordered sample in terms of\nthe random fields and couplings.", "category": "cond-mat_dis-nn" }, { "text": "Comment on \"Scaling behavior of classical wave transport in mesoscopic\n media at the localization transition\": We emphasize the importance of the position dependence of the diffusion\ncoefficient D(r) in the self-consistent theory of localization and argue that\nthe scaling law T ~ ln(L)/L^2 obtained by Cheung and Zhang [Phys. Rev. B 72,\n235102 (2005)] for the average transmission coefficient T of a disordered slab\nof thickness L at the localization transition is an artifact of replacing D(r)\nby its harmonic mean. The correct scaling T ~ 1/L^2 is obtained by properly\ntreating the position dependence of D(r).", "category": "cond-mat_dis-nn" }, { "text": "Many-Body-Localization Transition : strong multifractality spectrum for\n matrix elements of local operators: For short-ranged disordered quantum models in one dimension, the\nMany-Body-Localization is analyzed via the adaptation to the Many-Body context\n[M. Serbyn, Z. Papic and D.A. Abanin, PRX 5, 041047 (2015)] of the Thouless\npoint of view on the Anderson transition : the question is whether a local\ninteraction between two long chains is able to reshuffle completely the\neigenstates (Delocalized phase with a volume-law entanglement) or whether the\nhybridization between tensor states remains limited (Many-Body-Localized Phase\nwith an area-law entanglement). The central object is thus the level of\nHybridization induced by the matrix elements of local operators, as compared\nwith the difference of diagonal energies. The multifractal analysis of these\nmatrix elements of local operators is used to analyze the corresponding\nstatistics of resonances. Our main conclusion is that the critical point is\ncharacterized by the Strong-Multifractality Spectrum $f(0 \\leq \\alpha \\leq\n2)=\\frac{\\alpha}{2}$, well known in the context of Anderson Localization in\nspaces of effective infinite dimensionality, where the size of the Hilbert\nspace grows exponentially with the volume. Finally, the possibility of a\ndelocalized non-ergodic phase near criticality is discussed.", "category": "cond-mat_dis-nn" }, { "text": "Laser beam filamentation in fractal aggregates: We investigate filamentation of a cw laser beam in soft matter such as\ncolloidal suspensions and fractal gels. The process, driven by\nelectrostriction, is strongly affected by material properties, which are taken\ninto account via the static structure factor, and have impact on the statistics\nof the light filaments.", "category": "cond-mat_dis-nn" }, { "text": "Laser beam filamentation in fractal aggregates: We investigate filamentation of a cw laser beam in soft matter such as\ncolloidal suspensions and fractal gels. The process, driven by\nelectrostriction, is strongly affected by material properties, which are taken\ninto account via the static structure factor, and have impact on the statistics\nof the light filaments.", "category": "cond-mat_dis-nn" }, { "text": "Capillary forces in the acoustics of patchy-saturated porous media: A linearized theory of the acoustics of porous elastic formations, such as\nrocks, saturated with two different viscous fluids is generalized to take into\naccount a pressure discontinuity across the fluid boundaries. The latter can\narise due to the surface tension of the membrane separating the fluids. We show\nthat the frequency-dependent bulk modulus $\\tilde{K}(\\omega)$ for wave lengths\nlonger than the characteristic structural dimensions of the fluid patches has a\nsimilar analytic behavior as in the case of a vanishing membrane stiffness and\ndepends on the same parameters of the fluid-distribution topology. The effect\nof the capillary stiffness can be accounted by renormalizing the coefficients\nof the leading terms in the low-frequency asymptotic of $\\tilde{K}(\\omega)$.", "category": "cond-mat_dis-nn" }, { "text": "Extremal statistics of entanglement eigenvalues can track the many-body\n localized to ergodic transition: Some interacting disordered many-body systems are unable to thermalize when\nthe quenched disorder becomes larger than a threshold value. Although several\nproperties of nonzero energy density eigenstates (in the middle of the\nmany-body spectrum) exhibit a qualitative change across this many-body\nlocalization (MBL) transition, many of the commonly-used diagnostics only do so\nover a broad transition regime. Here, we provide evidence that the transition\ncan be located precisely even at modest system sizes by sharply-defined changes\nin the distribution of extremal eigenvalues of the reduced density matrix of\nsubsystems. In particular, our results suggest that $p* = \\lim_{\\lambda_2\n\\rightarrow \\ln(2)^{+}}P_2(\\lambda_2)$, where $P_2(\\lambda_2)$ is the\nprobability distribution of the second lowest entanglement eigenvalue\n$\\lambda_2$, behaves as an ''order-parameter'' for the MBL phase: $p*> 0$ in\nthe MBL phase, while $p* = 0$ in the ergodic phase with thermalization. Thus,\nin the MBL phase, there is a nonzero probability that a subsystem is entangled\nwith the rest of the system only via the entanglement of one subsystem qubit\nwith degrees of freedom outside the region. In contrast, this probability\nvanishes in the thermal phase.", "category": "cond-mat_dis-nn" }, { "text": "Information on mean, fluctuation and synchrony conveyed by a population\n of firing neurons: A population of firing neurons is expected to carry not only mean firing rate\nbut also its fluctuation and synchrony among neurons. In order to examine this\npossibility, we have studied responses of neuronal ensembles to three kinds of\ninputs: mean-, fluctuation- and synchrony-driven inputs. The generalized\nrate-code model including additive and multiplicative noise (H. Hasegawa, Phys.\nRev. E {\\bf 75}, 051904 (2007)) has been studied by direct simulations (DSs)\nand the augmented moment method (AMM) in which equations of motion for mean\nfiring rate, fluctuation and synchrony are derived. Results calculated by the\nAMM are in good agreement with those by DSs. The independent component analysis\n(ICA) of our results has shown that mean firing rate, fluctuation (or\nvariability) and synchrony may carry independent information in the population\nrate-code model. The input-output relation of mean firing rates is shown to\nhave higher sensitivity for larger multiplicative noise, as recently observed\nin prefrontal cortex. A comparison is made between results obtained by the\nintegrate-and-fire (IF) model and our rate-code model. The relevance of our\nresults to experimentally obtained data is also discussed.", "category": "cond-mat_dis-nn" }, { "text": "Phase diagram of superfluid 3He in \"nematically ordered\" aerogel: Results of experiments with liquid 3He immersed in a new type of aerogel are\ndescribed. This aerogel consists of Al2O3 strands which are nearly parallel to\neach other, so we call it as a \"nematically ordered\" aerogel. At all used\npressures a superfluid transition was observed and a superfluid phase diagram\nwas measured. Possible structures of the observed superfluid phases are\ndiscussed.", "category": "cond-mat_dis-nn" }, { "text": "Two-dimensional systems of elongated particles: From diluted to dense: This chapter is devoted to the analysis of jamming and percolation behavior\nof two-dimensional systems of elongated particles. We consider both continuous\nand discrete spaces (with the special attention to the square lattice), as well\nthe systems with isotropically deposited and aligned particles. Overviews of\ndifferent analytical and computational methods and main results are presented.", "category": "cond-mat_dis-nn" }, { "text": "Self-consistent study of Anderson localization in the Anderson-Hubbard\n model in two and three dimensions: We consider the change in electron localization due to the presence of\nelectron-electron repulsion in the \\HA model. Taking into account local\nMott-Hubbard physics and static screening of the disorder potential, the system\nis mapped onto an effective single-particle Anderson model, which is studied\nwithin the self-consistent theory of electron localization. We find rich\nnonmonotonic behavior of the localization length $\\xi$ in two-dimensional\nsystems, including an interaction-induced exponential enhancement of $\\xi$ for\nsmall and intermediate disorders although $\\xi$ remains finite. In three\ndimensions we identify for half filling a Mott-Hubbard-assisted Anderson\nlocalized phase existing between the metallic and the Mott-Hubbard-gapped\nphases. For small $U$ there is re-entrant behavior from the Anderson localized\nphase to the metallic phase.", "category": "cond-mat_dis-nn" }, { "text": "Monte Carlo Simulations of a Generalized n--spin facilitated kinetic\n Ising Model: A kinetic Ising model is analyzed where spin variables correspond to lattice\ncells with mobile or immobile particles. Introducing additional restrictions\nfor the flip processes according to the n-spin facilitated kinetic Ising model\nand using Monte Carlo methods we study the freezing process under the influence\nof an additional nearest-neighbor interaction. The stretched exponential decay\nof the auto-correlation function is observed and the exponent $\\gamma$ as well\nas the relaxation time are determined depending on the activation energy $h$\nand the short range coupling $J$. The magnetization corresponding to the\ndensity of immobile particles is found to be the controlling parameter for the\ndynamic evolution.", "category": "cond-mat_dis-nn" }, { "text": "Can Local Stress Enhancement Induce Stability in Fracture Processes?\n Part II: The Shielding Effect: We use the local load sharing fiber bundle model to demonstrate a shielding\neffect where strong fibers protect weaker ones. This effect exists due to the\nlocal stress enhancement around broken fibers in the local load sharing model,\nand it is therefore not present in the equal load sharing model. The shielding\neffect is prominent only after the initial disorder-driven part of the fracture\nprocess has finished, and if the fiber bundle has not reached catastrophic\nfailure by this point, then the shielding increases the critical damage of the\nsystem, compared to equal load sharing. In this sense, the local stress\nenhancement may make the fracture process more stable, but at the cost of\nreduced critical force.", "category": "cond-mat_dis-nn" }, { "text": "Eight orders of dynamical clusters and hard-spheres in the glass\n transition: The nature may be disclosed that the glass transition is only determined by\nthe intrinsic 8 orders of instant 2-D mosaic geometric structures, without any\npresupposition and relevant parameter. An interface excited state on the\ngeometric structures comes from the additional Lindemann distance increment,\nwhich is a vector with 8 orders of relaxation times, 8 orders of additional\nrestoring force moment (ARFM), quantized energy and extra volume. Each order of\nanharmonic ARFM gives rise to an additional position-asymmetry on a 2-D\nprojection plane of a reference particle, thus, in removing additional\nposition-asymmetry, the 8 orders of 2-D clusters and hard-spheres accompanied\nwith the 4 excited interface relaxations of the reference particle have been\nillustrated. Dynamical behavior comes of the slow inverse energy cascade to\ngenerate 8 orders of clusters, to thaw a solid-domain, and the fast cascade to\nrelax tension and rearrange structure. This model provides a unified mechanism\nto interpret hard-sphere, compacting cluster, free volume, cage, jamming\nbehaviors, geometrical frustration, reptation, Ising model, breaking solid\nlattice, percolation, cooperative migration and orientation, critical\nentanglement chain length and structure rearrangements. It also directly\ndeduces a series of quantitative values for the average energy of cooperative\nmigration in one direction, localized energy independent of temperature and the\nactivation energy to break solid lattice. In a flexible polymer system, there\nare all 320 different interface excited states that have the same quantized\nexcited energy but different interaction times, relaxation times and phases.\nThe quantized excited energy is about 6.4 k = 0.55meV.", "category": "cond-mat_dis-nn" }, { "text": "Biased doped silicene as a source for advanced electronics: Restructuring of electronic spectrum in a buckled silicene monolayer under\nsome applied voltage between its two sublattices and in presence of certain\nimpurity atoms is considered. A special attention is given to formation of\nlocalized impurity levels within the band gap and the to their collectivization\nat finite impurity concentration. It is shown that a qualitative restructuring\nof quasiparticle spectrum within the initial band gap and then specific\nmetal-insulator phase transitions are possible for such disordered system and\ncan be effectively controlled by variation of the electric field bias at given\nimpurity perturbation potential and concentration. Since these effects are\nexpected at low impurity concentrations but at not too low temperatures, they\ncan be promising for practical applications in nanoelectronics devices.", "category": "cond-mat_dis-nn" }, { "text": "Eigenstate phases with finite on-site non-Abelian symmetry: We study the eigenstate phases of disordered spin chains with on-site finite\nnon-Abelian symmetry. We develop a general formalism based on standard group\ntheory to construct local spin Hamiltonians invariant under any on-site\nsymmetry. We then specialize to the case of the simplest non-Abelian group,\n$S_3$, and numerically study a particular two parameter spin-1 Hamiltonian. We\nobserve a thermal phase and a many-body localized phase with a spontaneous\nsymmetry breaking (SSB) from $S_3$ to $\\mathbb{Z}_3$ in our model Hamiltonian.\nWe diagnose these phases using full entanglement distributions and level\nstatistics. We also use a spin-glass diagnostic specialized to detect\nspontaneous breaking of the $S_3$ symmetry down to $\\mathbb{Z}_3$. Our observed\nphases are consistent with the possibilities outlined by Potter and Vasseur\n[Phys. Rev. B 94, 224206 (2016)], namely thermal/ ergodic and spin-glass\nmany-body localized (MBL) phases. We also speculate about the nature of an\nintermediate region between the thermal and MBL+SSB regions where full $S_3$\nsymmetry exists.", "category": "cond-mat_dis-nn" }, { "text": "The Eigenvalue Analysis of the Density Matrix of 4D Spin Glasses\n Supports Replica Symmetry Breaking: We present a general and powerful numerical method useful to study the\ndensity matrix of spin models. We apply the method to finite dimensional spin\nglasses, and we analyze in detail the four dimensional Edwards-Anderson model\nwith Gaussian quenched random couplings. Our results clearly support the\nexistence of replica symmetry breaking in the thermodynamical limit.", "category": "cond-mat_dis-nn" }, { "text": "Topological phase transitions in random Kitaev $\u03b1$-chains: The topological phases of random Kitaev $\\alpha$-chains are labelled by the\nnumber of localized edge Majorana Zero Modes. The critical lines between these\nphases thus correspond to delocalization transitions for these localized edge\nMajorana Zero Modes. For the random Kitaev chain with next-nearest couplings,\nwhere there are three possible topological phases $n=0,1,2$, the two Lyapunov\nexponents of Majorana Zero Modes are computed for a specific solvable case of\nCauchy disorder, in order to analyze how the phase diagram evolves as a\nfunction of the disorder strength. In particular, the direct phase transition\nbetween the phases $n=0$ and $n=2$ is possible only in the absence of disorder,\nwhile the presence of disorder always induces an intermediate phase $n=1$, as\nfound previously via numerics for other distributions of disorder.", "category": "cond-mat_dis-nn" }, { "text": "Strong Griffiths singularities in random systems and their relation to\n extreme value statistics: We consider interacting many particle systems with quenched disorder having\nstrong Griffiths singularities, which are characterized by the dynamical\nexponent, z, such as random quantum systems and exclusion processes. In several\nd=1 and d=2 dimensional problems we have calculated the inverse time-scales,\nt^{-1}, in finite samples of linear size, L, either exactly or numerically. In\nall cases, having a discrete symmetry, the distribution function, P(t^{-1},L),\nis found to depend on the variable, u=t^{-1}L^{z/d}, and to be universal given\nby the limit distribution of extremes of independent and identically\ndistributed random numbers. This finding is explained in the framework of a\nstrong disorder renormalization group approach when, after fast degrees of\nfreedom are decimated out the system is transformed into a set of\nnon-interacting localized excitations. The Frechet distribution of P(t^{-1},L)\nis expected to hold for all random systems having a strong disorder fixed\npoint, in which the Griffiths singularities are dominated by disorder\nfluctuations.", "category": "cond-mat_dis-nn" }, { "text": "Diluted neural networks with adapting and correlated synapses: We consider the dynamics of diluted neural networks with clipped and adapting\nsynapses. Unlike previous studies, the learning rate is kept constant as the\nconnectivity tends to infinity: the synapses evolve on a time scale\nintermediate between the quenched and annealing limits and all orders of\nsynaptic correlations must be taken into account. The dynamics is solved by\nmean-field theory, the order parameter for synapses being a function. We\ndescribe the effects, in the double dynamics, due to synaptic correlations.", "category": "cond-mat_dis-nn" }, { "text": "Machine learning magnetic parameters from spin configurations: Hamiltonian parameter estimation is crucial in condensed matter physics, but\ntime and cost consuming in terms of resources used. With advances in\nobservation techniques, high-resolution images with more detailed information\nare obtained, which can serve as an input to machine learning (ML) algorithms\nto extract Hamiltonian parameters. However, the number of labeled images is\nrather limited. Here, we provide a protocol for Hamiltonian parameter\nestimation based on a machine learning architecture, which is trained on a\nsmall amount of simulated images and applied to experimental spin configuration\nimages. Sliding windows on the input images enlarges the number of training\nimages; therefore we can train well a neural network on a small dataset of\nsimulated images which are generated adaptively using the same external\nconditions such as temperature and magnetic field as the experiment. The neural\nnetwork is applied to the experimental image and estimates magnetic parameters\nefficiently. We demonstrate the success of the estimation by reproducing the\nsame configuration from simulation and predict a hysteresis loop accurately.\nOur approach paves a way to a stable and general parameter estimation.", "category": "cond-mat_dis-nn" }, { "text": "A Green's function approach to transmission of massless Dirac fermions\n in graphene through an array of random scatterers: We consider the transmission of massless Dirac fermions through an array of\nshort range scatterers which are modeled as randomly positioned $\\delta$-\nfunction like potentials along the x-axis. We particularly discuss the\ninterplay between disorder-induced localization that is the hallmark of a\nnon-relativistic system and two important properties of such massless Dirac\nfermions, namely, complete transmission at normal incidence and periodic\ndependence of transmission coefficient on the strength of the barrier that\nleads to a periodic resonant transmission. This leads to two different types of\nconductance behavior as a function of the system size at the resonant and the\noff-resonance strengths of the delta function potential. We explain this\nbehavior of the conductance in terms of the transmission through a pair of such\nbarriers using a Green's function based approach. The method helps to\nunderstand such disordered transport in terms of well known optical phenomena\nsuch as Fabry Perot resonances.", "category": "cond-mat_dis-nn" }, { "text": "Absence of Mobility Edge in Short-range Uncorrelated Disordered Model:\n Coexistence of Localized and Extended States: Unlike the well-known Mott's argument that extended and localized states\nshould not coexist at the same energy in a generic random potential, we provide\nan example of a nearest-neighbor tight-binding disordered model which carries\nboth localized and extended states without forming the mobility edge (ME).\nUnexpectedly, this example appears to be given by a well-studied\n$\\beta$-ensemble with independently distributed random diagonal potential and\ninhomogeneous kinetic hopping terms. In order to analytically tackle the\nproblem, we locally map the above model to the 1D Anderson model with\nmatrix-size- and position-dependent hopping and confirm the coexistence of\nlocalized and extended states, which is shown to be robust to the perturbations\nof both potential and kinetic terms due to the separation of the above states\nin space. In addition, the mapping shows that the extended states are\nnon-ergodic and allows to analytically estimate their fractal dimensions.", "category": "cond-mat_dis-nn" }, { "text": "Competition between Barrier- and Entropy-Driven Activation in Glasses: In simplified models of glasses we clarify the existence of two different\nkinds of activated dynamics, which coexist, with one of the two dominating over\nthe other. One is the energy barrier hopping that is typically used to picture\nactivation, and the other one, which we call entropic activation, is driven by\nthe scarcity of convenient directions. When entropic activation dominates, the\nheight of the energy barriers is no longer the decisive to describe the\nsystem's slowdown. In our analysis, dominance of one mechanism over the other\ndepends on the shape of the density of states and temperature. We also find\nthat at low temperatures a phase transition between the two kinds of activation\ncan occur. Our framework can be used to harmonize the facilitation and\nthermodynamic pictures of the slowdown of glasses.", "category": "cond-mat_dis-nn" }, { "text": "Non-equilibrium criticality and efficient exploration of glassy\n landscapes with memory dynamics: Spin glasses are notoriously difficult to study both analytically and\nnumerically due to the presence of frustration and metastability. Their highly\nnon-convex landscapes require collective updates to explore efficiently.\nCurrently, most state-of-the-art algorithms rely on stochastic spin clusters to\nperform non-local updates, but such \"cluster algorithms\" lack general\nefficiency. Here, we introduce a non-equilibrium approach for simulating spin\nglasses based on classical dynamics with memory. By simulating various classes\nof 3d spin glasses (Edwards-Anderson, partially-frustrated, and\nfully-frustrated models), we find that memory dynamically promotes critical\nspin clusters during time evolution, in a self-organizing manner. This\nfacilitates an efficient exploration of the low-temperature phases of spin\nglasses.", "category": "cond-mat_dis-nn" }, { "text": "Quantum dynamics in strongly driven random dipolar magnets: The random dipolar magnet LiHo$_x$Y$_{1-x}$F$_4$ enters a strongly frustrated\nregime for small Ho$^{3+}$ concentrations with $x<0.05$. In this regime, the\nmagnetic moments of the Ho$^{3+}$ ions experience small quantum corrections to\nthe common Ising approximation of LiHo$_x$Y$_{1-x}$F$_4$, which lead to a\n$Z_2$-symmetry breaking and small, degeneracy breaking energy shifts between\ndifferent eigenstates. Here we show that destructive interference between two\nalmost degenerate excitation pathways burns spectral holes in the magnetic\nsusceptibility of strongly driven magnetic moments in LiHo$_x$Y$_{1-x}$F$_4$.\nSuch spectral holes in the susceptibility, microscopically described in terms\nof Fano resonances, can already occur in setups of only two or three frustrated\nmoments, for which the driven level scheme has the paradigmatic\n$\\Lambda$-shape. For larger clusters of magnetic moments, the corresponding\nlevel schemes separate into almost isolated many-body $\\Lambda$-schemes, in the\nsense that either the transition matrix elements between them are negligibly\nsmall or the energy difference of the transitions is strongly off-resonant to\nthe drive. This enables the observation of Fano resonances, caused by many-body\nquantum corrections to the common Ising approximation also in the thermodynamic\nlimit. We discuss its dependence on the driving strength and frequency as well\nas the crucial role that is played by lattice dissipation.", "category": "cond-mat_dis-nn" }, { "text": "Phase boundary near a magnetic percolation transition: Motivated by recent experimental observations [Phys. Rev. 96, 020407 (2017)]\non hexagonal ferrites, we revisit the phase diagrams of diluted magnets close\nto the lattice percolation threshold. We perform large-scale Monte Carlo\nsimulations of XY and Heisenberg models on both simple cubic lattices and\nlattices representing the crystal structure of the hexagonal ferrites. Close to\nthe percolation threshold $p_c$, we find that the magnetic ordering temperature\n$T_c$ depends on the dilution $p$ via the power law $T_c \\sim |p-p_c|^\\phi$\nwith exponent $\\phi=1.09$, in agreement with classical percolation theory.\nHowever, this asymptotic critical region is very narrow, $|p-p_c| \\lesssim\n0.04$. Outside of it, the shape of the phase boundary is well described, over a\nwide range of dilutions, by a nonuniversal power law with an exponent somewhat\nbelow unity. Nonetheless, the percolation scenario does not reproduce the\nexperimentally observed relation $T_c \\sim (x_c -x)^{2/3}$ in\nPbFe$_{12-x}$Ga$_x$O$_{19}$. We discuss the generality of our findings as well\nas implications for the physics of diluted hexagonal ferrites.", "category": "cond-mat_dis-nn" }, { "text": "Fidelity susceptibility in Gaussian Random Ensembles: The fidelity susceptibility measures sensitivity of eigenstates to a change\nof an external parameter. It has been fruitfully used to pin down quantum phase\ntransitions when applied to ground states (with extensions to thermal states).\nHere we propose to use the fidelity susceptibility as a useful dimensionless\nmeasure for complex quantum systems. We find analytically the fidelity\nsusceptibility distributions for Gaussian orthogonal and unitary universality\nclasses for arbitrary system size. The results are verified by a comparison\nwith numerical data.", "category": "cond-mat_dis-nn" }, { "text": "Universality of phonon transport in surface-roughness dominated\n nanowires: We analyze, both theoretically and numerically, the temperature dependent\nthermal conductivity \\k{appa} of two-dimensional nanowires with surface\nroughness. Although each sample is characterized by three independent\nparameters - the diameter (width) of the wire, the correlation length and\nstrength of the surface corrugation - our theory predicts that there exists a\nuniversal regime where \\k{appa} is a function of a single combination of all\nthree model parameters. Numerical simulations of propagation of acoustic\nphonons across thin wires confirm this universality and predict a d 1/2\ndependence of \\k{appa} on the diameter d.", "category": "cond-mat_dis-nn" }, { "text": "A glassy phase in quenched disordered graphene and crystalline membranes: We investigate the flat phase of $D$-dimensional crystalline membranes\nembedded in a $d$-dimensional space and submitted to both metric and curvature\nquenched disorders using a nonperturbative renormalization group approach. We\nidentify a second order phase transition controlled by a finite-temperature,\nfinite-disorder fixed point unreachable within the leading order of\n$\\epsilon=4-D$ and $1/d$ expansions. This critical point divides the flow\ndiagram into two basins of attraction: that associated to the\nfinite-temperature fixed point controlling the long distance behaviour of\ndisorder-free membranes and that associated to the zero-temperature,\nfinite-disorder fixed point. Our work thus strongly suggests the existence of a\nwhole low-temperature glassy phase for quenched disordered graphene,\ngraphene-like compounds and, more generally, crystalline membranes.", "category": "cond-mat_dis-nn" }, { "text": "Possibly Exact Solution for the Multicritical Point of\n Finite-Dimensional Spin Glasses: After briefly describing the present status of the spin glass theory, we\npresent a conjecture on the exact location of the multicritical point in the\nphase diagram of finite-dimensional spin glasses. The theory enables us to\nunderstand in a unified way many numerical results for two-, three- and\nfour-dimensional models including the +-J Ising model, random Potts model,\nrandom lattice gauge theory, and random Zq model. It is also suggested from the\nsame theoretical framework that models with symmetric distribution of\nrandomness in exchange interaction have no finite-temperature transition on the\nsquare lattice.", "category": "cond-mat_dis-nn" }, { "text": "Random Mass Dirac Fermions in Doped Spin-Peierls and Spin-Ladder\n systems: One-Particle Properties and Boundary Effects: Quasi-one-dimensional spin-Peierls and spin-ladder systems are characterized\nby a gap in the spin-excitation spectrum, which can be modeled at low energies\nby that of Dirac fermions with a mass. In the presence of disorder these\nsystems can still be described by a Dirac fermion model, but with a random\nmass. Some peculiar properties, like the Dyson singularity in the density of\nstates, are well known and attributed to creation of low-energy states due to\nthe disorder. We take one step further and study single-particle correlations\nby means of Berezinskii's diagram technique. We find that, at low energy\n$\\epsilon$, the single-particle Green function decays in real space like\n$G(x,\\epsilon) \\propto (1/x)^{3/2}$. It follows that at these energies the\ncorrelations in the disordered system are strong -- even stronger than in the\npure system without the gap. Additionally, we study the effects of boundaries\non the local density of states. We find that the latter is logarithmically (in\nthe energy) enhanced close to the boundary. This enhancement decays into the\nbulk as $1/\\sqrt{x}$ and the density of states saturates to its bulk value on\nthe scale $L_\\epsilon \\propto \\ln^2 (1/\\epsilon)$. This scale is different from\nthe Thouless localization length $\\lambda_\\epsilon\\propto\\ln (1/\\epsilon)$. We\nalso discuss some implications of these results for the spin systems and their\nrelation to the investigations based on real-space renormalization group\napproach.", "category": "cond-mat_dis-nn" }, { "text": "Finite-size corrections in the random assignment problem: We analytically derive, in the context of the replica formalism, the first\nfinite size corrections to the average optimal cost in the random assignment\nproblem for a quite generic distribution law for the costs. We show that, when\nmoving from a power-law distribution to a $\\Gamma$ distribution, the leading\ncorrection changes both in sign and in its scaling properties. We also examine\nthe behavior of the corrections when approaching a $\\delta$-function\ndistribution. By using a numerical solution of the saddle-point equations, we\nprovide predictions that are confirmed by numerical simulations.", "category": "cond-mat_dis-nn" }, { "text": "Temperature-dependent disorder and magnetic field driven disorder:\n experimental observations for doped GaAs/AlGaAs quantum well structures: We report experimental studies of conductance and magnetoconductance of\nGaAs/AlGaAs quantum well structures where both wells and barriers are doped by\nacceptor impurity Be. Temperature dependence of conductance demonstrate a\nnon-monotonic behavior at temperatures around 100 K. At small temperatures\n(less than 10 K) we observed strong negative magnetoresistance at moderate\nmagnetic field which crossed over to positive magnetoresistance at very strong\nmagnetic fields and was completely suppressed with an increase of temperature.\nWe ascribe these unusual features to effects of temperature and magnetic field\non a degree of disorder. The temperature dependent disorder is related to\ncharge redistribution between different localized states with an increase of\ntemperature. The magnetic field dependent disorder is also related by charge\nredistribution between different centers, however in this case an important\nrole is played by the doubly occupied states of the upper Hubbard band, their\noccupation being sensitive to magnetic field due to on-site spin correlations.\nThe detailed theoretical model is present.", "category": "cond-mat_dis-nn" }, { "text": "T=0 phase diagram and nature of domains in ultrathin ferromagnetic films\n with perpendicular anisotropy: We present the complete zero temperature phase diagram of a model for\nultrathin films with perpendicular anisotropy. The whole parameter space of\nrelevant coupling constants is studied in first order anisotropy approximation.\nBecause the ground state is known to be formed by perpendicular stripes\nseparated by Bloch walls, a standard variational approach is used, complemented\nwith specially designed Monte Carlo simulations. We can distinguish four\nregimes according to the different nature of striped domains: a high anisotropy\nIsing regime with sharp domain walls, a saturated stripe regime with thicker\nwalls inside which an in-plane component of the magnetization develops, a\nnarrow canted-like regime, characterized by a sinusoidal variation of both the\nin-plane and the out of plane magnetization components, which upon further\ndecrease of the anisotropy leads to an in-plane ferromagnetic state via a spin\nreorientation transition (SRT). The nature of domains and walls are described\nin some detail together with the variation of domain width with anisotropy, for\nany value of exchange and dipolar interactions. Our results, although strictly\nvalid at $T=0$, can be valuable for interpreting data on the evolution of\ndomain width at finite temperature, a still largely open problem.", "category": "cond-mat_dis-nn" }, { "text": "Normal mode analysis of spectra of random networks: Several spectral fluctuation measures of random matrix theory (RMT) have been\napplied in the study of spectral properties of networks. However, the\ncalculation of those statistics requires performing an unfolding procedure,\nwhich may not be an easy task. In this work, network spectra are interpreted as\ntime series, and we show how their short and long-range correlations can be\ncharacterized without implementing any previous unfolding. In particular, we\nconsider three different representations of Erd\\\"os-R\\'enyi (ER) random\nnetworks: standard ER networks, ER networks with random-weighted self-edges,\nand fully random-weighted ER networks. In each case, we apply singular value\ndecomposition (SVD) such that the spectra are decomposed in trend and\nfluctuation normal modes. We obtain that the fluctuation modes exhibit a clear\ncrossover between the Poisson and the Gaussian orthogonal ensemble statistics\nwhen increasing the average degree of ER networks. Moreover, by using the trend\nmodes, we perform a data-adaptive unfolding to calculate, for comparison\npurposes, traditional fluctuation measures such as the nearest neighbor spacing\ndistribution, number variance $\\Sigma$2, as well as $\\Delta$3 and {\\delta}n\nstatistics. The thorough comparison of RMT short and long-range correlation\nmeasures make us identify the SVD method as a robust tool for characterizing\nrandom network spectra.", "category": "cond-mat_dis-nn" }, { "text": "The Approximate Invariance of the Average Number of Connections for the\n Continuum Percolation of Squares at Criticality: We perform Monte Carlo simulations to determine the average excluded area\n$$ of randomly oriented squares, randomly oriented widthless sticks and\naligned squares in two dimensions. We find significant differences between our\nresults for randomly oriented squares and previous analytical results for the\nsame. The sources of these differences are explained. Using our results for\n$$ and Monte Carlo simulation results for the percolation threshold, we\nestimate the mean number of connections per object $B_c$ at the percolation\nthreshold for squares in 2-D. We study systems of squares that are allowed\nrandom orientations within a specified angular interval. Our simulations show\nthat the variation in $B_c$ is within 1.6% when the angular interval is varied\nfrom 0 to $\\pi/2$.", "category": "cond-mat_dis-nn" }, { "text": "Backtracking Dynamical Cavity Method: The cavity method is one of the cornerstones of the statistical physics of\ndisordered systems such as spin glasses and other complex systems. It is able\nto analytically and asymptotically exactly describe the equilibrium properties\nof a broad range of models. Exact solutions for dynamical, out-of-equilibrium\nproperties of disordered systems are traditionally much harder to obtain. Even\nvery basic questions such as the limiting energy of a fast quench are so far\nopen. The dynamical cavity method partly fills this gap by considering short\ntrajectories and leveraging the static cavity method. However, being limited to\na couple of steps forward from the initialization it typically does not capture\ndynamical properties related to attractors of the dynamics. We introduce the\nbacktracking dynamical cavity method that instead of analysing the trajectory\nforward from initialization, analyses trajectories that are found by tracking\nthem backward from attractors. We illustrate that this rather elementary twist\non the dynamical cavity method leads to new insight into some of the very basic\nquestions about the dynamics of complex disordered systems. This method is as\nversatile as the cavity method itself and we hence anticipate that our paper\nwill open many avenues for future research of dynamical, out-of-equilibrium,\nproperties in complex systems.", "category": "cond-mat_dis-nn" }, { "text": "Low-frequency vibrational spectrum of mean-field disordered systems: We study a recently introduced and exactly solvable mean-field model for the\ndensity of vibrational states $\\mathcal{D}(\\omega)$ of a structurally\ndisordered system. The model is formulated as a collection of disordered\nanharmonic oscillators, with random stiffness $\\kappa$ drawn from a\ndistribution $p(\\kappa)$, subjected to a constant field $h$ and interacting\nbilinearly with a coupling of strength $J$. We investigate the vibrational\nproperties of its ground state at zero temperature. When $p(\\kappa)$ is gapped,\nthe emergent $\\mathcal{D}(\\omega)$ is also gapped, for small $J$. Upon\nincreasing $J$, the gap vanishes on a critical line in the $(h,J)$ phase\ndiagram, whereupon replica symmetry is broken. At small $h$, the form of this\npseudogap is quadratic, $\\mathcal{D}(\\omega)\\sim\\omega^2$, and its modes are\ndelocalized, as expected from previously investigated mean-field spin glass\nmodels. However, we determine that for large enough $h$, a quartic pseudogap\n$\\mathcal{D}(\\omega)\\sim\\omega^4$, populated by localized modes, emerges, the\ntwo regimes being separated by a special point on the critical line. We thus\nuncover that mean-field disordered systems can generically display both a\nquadratic-delocalized and a quartic-localized spectrum at the glass transition.", "category": "cond-mat_dis-nn" }, { "text": "A Complex Network Analysis on The Eigenvalue Spectra of Random Spin\n Systems: Recent works have established a novel viewpoint that treats the eigenvalue\nspectra of disordered quantum systems as time-series, and corresponding\nalgorithms such as singular-value-decomposition has proven its advantage in\nstudying subtle physical quantities like Thouless energy and non-ergodic\nextended regime. On the other hand, algorithms from complex networks have long\nbeen known as a powerful tool to study highly nonlinear time-series. In this\nwork, we combine these two ideas together. Using the particular algorithm\ncalled visibility graph (VG) that transforms the eigenvalue spectra of a random\nspin system into complex networks, it's shown the degree distribution of the\nresulting network is capable of signaturing the eigenvalue evolution during the\nthermal to many-body localization transition, and the networks in the thermal\nphase have a small-world structure. We further show these results are robust\neven when the eigenvalues are incomplete with missing levels, which reveals the\nadvantage of the VG algorithm.", "category": "cond-mat_dis-nn" }, { "text": "Analyses of kinetic glass transition in short-range attractive colloids\n based on time-convolutionless mode-coupling theory: The kinetic glass transition in short-range attractive colloids is\ntheoretically studied by time-convolutionless mode-coupling theory (TMCT). By\nnumerical calculations, TMCT is shown to recover all the remarkable features\npredicted by the mode-coupling theory for attractive colloids, namely the\nglass-liquid-glass reentrant, the glass-glass transition, and the higher-order\nsingularities. It is also demonstrated through the comparisons with the results\nof molecular dynamics for the binary attractive colloids that TMCT improves the\ncritical values of the volume fraction. In addition, a schematic model of three\ncontrol parameters is investigated analytically. It is thus confirmed that TMCT\ncan describe the glass-glass transition and higher-order singularities even in\nsuch a schematic model.", "category": "cond-mat_dis-nn" }, { "text": "Maximum-energy records in glassy energy landscapes: We study the evolution of the maximum energy $E_\\max(t)$ reached between time\n$0$ and time $t$ in the dynamics of simple models with glassy energy\nlandscapes, in instant quenches from infinite temperature to a target\ntemperature $T$. Through a detailed description of the activated dynamics, we\nare able to describe the evolution of $E_\\max(t)$ from short times, through the\naging regime, until after equilibrium is reached, thus providing a detailed\ndescription of the long-time dynamics. Finally, we compare our findings with\nnumerical simulations of the $p$-spin glass and show how the maximum energy\nrecord can be used to identify the threshold energy in this model.", "category": "cond-mat_dis-nn" }, { "text": "Destruction of Localization by Thermal Inclusions: Anomalous Transport\n and Griffiths Effects in the Anderson and Andr\u00e9-Aubry-Harper Models: We discuss and compare two recently proposed toy models for anomalous\ntransport and Griffiths effects in random systems near the Many-Body\nLocalization transitions: the random dephasing model, which adds thermal\ninclusions in an Anderson Insulator as local Markovian dephasing channels that\nheat up the system, and the random Gaussian Orthogonal Ensemble (GOE) approach\nwhich models them in terms of ensembles of random regular graphs. For these two\nsettings we discuss and compare transport and dissipative properties and their\nstatistics. We show that both types of dissipation lead to similar\nGriffiths-like phenomenology, with the GOE bath being less effective in\nthermalising the system due to its finite bandwidth. We then extend these\nmodels to the case of a quasi-periodic potential as described by the\nAndr\\'e-Aubry-Harper model coupled to random thermal inclusions, that we show\nto display, for large strength of the quasiperiodic potential, a similar\nphenomenology to the one of the purely random case. In particular, we show the\nemergence of subdiffusive transport and broad statistics of the local density\nof states, suggestive of Griffiths like effects arising from the interplay\nbetween quasiperiodic localization and random coupling to the baths.", "category": "cond-mat_dis-nn" }, { "text": "A frozen glass phase in the multi-index matching problem: The multi-index matching is an NP-hard combinatorial optimization problem;\nfor two indices it reduces to the well understood bipartite matching problem\nthat belongs to the polynomial complexity class. We use the cavity method to\nsolve the thermodynamics of the multi-index system with random costs. The phase\ndiagram is much richer than for the case of the bipartite matching problem: it\nshows a finite temperature phase transition to a completely frozen glass phase,\nsimilar to what happens in the random energy model. We derive the critical\ntemperature, the ground state energy density, and properties of the energy\nlandscape, and compare the results to numerical studies based on exact analysis\nof small systems.", "category": "cond-mat_dis-nn" }, { "text": "Spatio-temporal heterogeneity of entanglement in many-body localized\n systems: We propose a spatio-temporal characterization of the entanglement dynamics in\nmany-body localized (MBL) systems, which exhibits a striking resemblance with\ndynamical heterogeneity in classical glasses. Specifically, we find that the\nrelaxation times of local entanglement, as measured by the concurrence, are\nspatially correlated yielding a dynamical length scale for quantum\nentanglement. As a consequence of this spatio-temporal analysis, we observe\nthat the considered MBL system is made up of dynamically correlated clusters\nwith a size set by this entanglement length scale. The system decomposes into\ncompartments of different activity such as active regions with fast quantum\nentanglement dynamics and inactive regions where the dynamics is slow. We\nfurther find that the relaxation times of the on-site concurrence become\nbroader distributed and more spatially correlated, as disorder increases or the\nenergy of the initial state decreases. Through this spatio-temporal\ncharacterization of entanglement, our work unravels a previously unrecognized\nconnection between the behavior of classical glasses and the genuine quantum\ndynamics of MBL systems.", "category": "cond-mat_dis-nn" }, { "text": "Resistance distribution in the hopping percolation model: We study the distribution function, P(rho), of the effective resistance, rho,\nin two and three-dimensional random resistor network of linear size L in the\nhopping percolation model. In this model each bond has a conductivity taken\nfrom an exponential form \\sigma ~ exp(-kappa r), where kappa is a measure of\ndisorder, and r is a random number, 0< r < 1. We find that in both the usual\nstrong disorder regime L/kappa^{nu} > 1 (not sensitive to removal of any single\nbond) and the extreme disorder regime L/kappa^{nu} < 1 (very sensitive to such\na removal) the distribution depends only on L/kappa^{nu} and can be well\napproximated by a log-normal function with dispersion b kappa^nu/L, where b is\na coefficient which depends on the type of the lattice", "category": "cond-mat_dis-nn" }, { "text": "Coupled electron--heat transport in nonuniform thin film semiconductor\n structures: A theory of transverse electron transport coupled with heat transfer in\nsemiconductor thin films is developed conceptually modeling structures of\nmodern electronics. The transverse currents generate Joule heat with positive\nfeedback through thermally activated conductivity. This can lead to instability\nknown as thermal runaway, or hot spot, or reversible thermal breakdown. A\ntheory here is based on the optimum fluctuation method modified to describe\nsaddle stationary points determining the rate of such instabilities and\nconditions under which they evolve. Depending on the material and system\nparameters, the instabilities appear in a manner of phase transitions, similar\nto either nucleation or spinodal decomposition.", "category": "cond-mat_dis-nn" }, { "text": "Depinning exponents of the driven long-range elastic string: We perform a high-precision calculation of the critical exponents for the\nlong-range elastic string driven through quenched disorder at the depinning\ntransition, at zero temperature. Large-scale simulations are used to avoid\nfinite-size effects and to enable high precision. The roughness, growth, and\nvelocity exponents are calculated independently, and the dynamic and\ncorrelation length exponents are derived. The critical exponents satisfy known\nscaling relations and agree well with analytical predictions.", "category": "cond-mat_dis-nn" }, { "text": "Scale Invariance in Percolation Theory and Fractals: The properties of the similarity transformation in percolation theory in the\ncomplex plane of the percolation probability are studied. It is shown that the\npercolation problem on a two-dimensional square lattice reduces to the\nMandelbrot transformation, leading to a fractal behavior of the percolation\nprobability in the complex plane. The hierarchical chains of impedances,\nreducing to a nonlinear mapping of the impedance space onto itself, are\nstudied. An infinite continuation of the procedure leads to a fixed point. It\nis shown that the number of steps required to reach a neighborhood of this\npoint has a fractal distribution.", "category": "cond-mat_dis-nn" }, { "text": "Rapid algorithm for identifying backbones in the two-dimensional\n percolation model: We present a rapid algorithm for identifying the current-carrying backbone in\nthe percolation model. It applies to general two-dimensional graphs with open\nboundary conditions. Complemented by the modified Hoshen-Kopelman cluster\nlabeling algorithm, our algorithm identifies dangling parts using their local\nproperties. For planar graphs, it finds the backbone almost four times as fast\nas Tarjan's depth-first-search algorithm, and uses the memory of the same size\nas the modified Hoshen-Kopelman algorithm. Comparison with other algorithms for\nbackbone identification is addressed.", "category": "cond-mat_dis-nn" }, { "text": "Short-Range Spin Glasses: The Metastate Approach: We discuss the metastate, a probability measure on thermodynamic states, and\nits usefulness in addressing difficult questions pertaining to the statistical\nmechanics of systems with quenched disorder, in particular short-range spin\nglasses. The possible low-temperature structures of realistic (i.e.,\nshort-range) spin glass models are described, and a number of fundamental open\nquestions are presented.", "category": "cond-mat_dis-nn" }, { "text": "How to guess the inter magnetic bubble potential by using a simple\n perceptron ?: It is shown that magnetic bubble films behaviour can be described by using a\n2D super-Ising hamiltonian. Calculated hysteresis curves and magnetic domain\npatterns are successfully compared with experimental results taken in\nliterature. The reciprocal problem of finding paramaters of the super-Ising\nmodel to reproduce computed or experimental magnetic domain pictures is solved\nby using a perceptron neural network.", "category": "cond-mat_dis-nn" }, { "text": "Kovacs effect in solvable model glasses: The Kovacs protocol, based on the temperature shift experiment originally\nconceived by A.J. Kovacs and applied on glassy polymers, is implemented in an\nexactly solvable model with facilitated dynamics. This model is based on\ninteracting fast and slow modes represented respectively by spherical spins and\nharmonic oscillator variables. Due to this fundamental property and to slow\ndynamics, the model reproduces the characteristic non-monotonic evolution known\nas the ``Kovacs effect'', observed in polymers, spin glasses, in granular\nmaterials and models of molecular liquids, when similar experimental protocols\nare implemented.", "category": "cond-mat_dis-nn" }, { "text": "Non-equilibrium physics: from spin glasses to machine and neural\n learning: Disordered many-body systems exhibit a wide range of emergent phenomena\nacross different scales. These complex behaviors can be utilized for various\ninformation processing tasks such as error correction, learning, and\noptimization. Despite the empirical success of utilizing these systems for\nintelligent tasks, the underlying principles that govern their emergent\nintelligent behaviors remain largely unknown. In this thesis, we aim to\ncharacterize such emergent intelligence in disordered systems through\nstatistical physics. We chart a roadmap for our efforts in this thesis based on\ntwo axes: learning mechanisms (long-term memory vs. working memory) and\nlearning dynamics (artificial vs. natural). Throughout our journey, we uncover\nrelationships between learning mechanisms and physical dynamics that could\nserve as guiding principles for designing intelligent systems. We hope that our\ninvestigation into the emergent intelligence of seemingly disparate learning\nsystems can expand our current understanding of intelligence beyond neural\nsystems and uncover a wider range of computational substrates suitable for AI\napplications.", "category": "cond-mat_dis-nn" }, { "text": "On Renyi entropies characterizing the shape and the extension of the\n phase space representation of quantum wave functions in disordered systems: We discuss some properties of the generalized entropies, called Renyi\nentropies and their application to the case of continuous distributions. In\nparticular it is shown that these measures of complexity can be divergent,\nhowever, their differences are free from these divergences thus enabling them\nto be good candidates for the description of the extension and the shape of\ncontinuous distributions. We apply this formalism to the projection of wave\nfunctions onto the coherent state basis, i.e. to the Husimi representation. We\nalso show how the localization properties of the Husimi distribution on average\ncan be reconstructed from its marginal distributions that are calculated in\nposition and momentum space in the case when the phase space has no structure,\ni.e. no classical limit can be defined. Numerical simulations on a one\ndimensional disordered system corroborate our expectations.", "category": "cond-mat_dis-nn" }, { "text": "Optical computation of a spin glass dynamics with tunable complexity: Spin Glasses (SG) are paradigmatic models for physical, computer science,\nbiological and social systems. The problem of studying the dynamics for SG\nmodels is NP hard, i.e., no algorithm solves it in polynomial time. Here we\nimplement the optical simulation of a SG, exploiting the N segments of a\nwavefront shaping device to play the role of the spin variables, combining the\ninterference at downstream of a scattering material to implement the random\ncouplings between the spins (the J ij matrix) and measuring the light intensity\non a number P of targets to retrieve the energy of the system. By implementing\na plain Metropolis algorithm, we are able to simulate the spin model dynamics,\nwhile the degree of complexity of the potential energy landscape and the region\nof phase diagram explored is user-defined acting on the ratio the P/N = \\alpha.\nWe study experimentally, numerically and analytically this peculiar system\ndisplaying a paramagnetic, a ferromagnetic and a SG phase, and we demonstrate\nthat the transition temperature T g to the glassy phase from the paramagnetic\nphase grows with \\alpha. With respect to standard in silico approach, in the\noptical SG interaction terms are realized simultaneously when the independent\nlight rays interferes at the target screen, enabling inherently parallel\nmeasurements of the energy, rather than computations scaling with N as in\npurely in silico simulations.", "category": "cond-mat_dis-nn" }, { "text": "Eigenvalue spectra of large correlated random matrices: Using the diagrammatic method, we derive a set of self-consistent equations\nthat describe eigenvalue distributions of large correlated asymmetric random\nmatrices. The matrix elements can have different variances and be correlated\nwith each other. The analytical results are confirmed by numerical simulations.\nThe results have implications for the dynamics of neural and other biological\nnetworks where plasticity induces correlations in the connection strengths\nwithin the network. We find that the presence of correlations can have a major\nimpact on network stability.", "category": "cond-mat_dis-nn" }, { "text": "Absence of a structural glass phase in a monoatomic model liquid\n predicted to undergo an ideal glass transition: We study numerically a monodisperse model of interacting classical particles\npredicted to exhibit a static liquid-glass transition. Using a dynamical Monte\nCarlo method we show that the model does not freeze into a glassy phase at low\ntemperatures. Instead, depending on the choice of the hard-core radius for the\nparticles the system either collapses trivially or a polycrystalline hexagonal\nstructure emerges.", "category": "cond-mat_dis-nn" }, { "text": "Localization of Electronic Wave Functions on Quasiperiodic Lattices: We study electronic eigenstates on quasiperiodic lattices using a\ntight-binding Hamiltonian in the vertex model. In particular, the\ntwo-dimensional Penrose tiling and the three-dimensional icosahedral\nAmmann-Kramer tiling are considered. Our main interest concerns the decay form\nand the self-similarity of the electronic wave functions, which we compute\nnumerically for periodic approximants of the perfect quasiperiodic structure.\nIn order to investigate the suggested power-law localization of states, we\ncalculate their participation numbers and structural entropy. We also perform a\nmultifractal analysis of the eigenstates by standard box-counting methods. Our\nresults indicate a rather different behaviour of the two- and the\nthree-dimensional systems. Whereas the eigenstates on the Penrose tiling\ntypically show power-law localization, this was not observed for the\nicosahedral tiling.", "category": "cond-mat_dis-nn" }, { "text": "Phase ordering on small-world networks with nearest-neighbor edges: We investigate global phase coherence in a system of coupled oscillators on a\nsmall-world networks constructed from a ring with nearest-neighbor edges. The\neffects of both thermal noise and quenched randomness on phase ordering are\nexamined and compared with the global coherence in the corresponding \\xy model\nwithout quenched randomness. It is found that in the appropriate regime phase\nordering emerges at finite temperatures, even for a tiny fraction of shortcuts.\nNature of the phase transition is also discussed.", "category": "cond-mat_dis-nn" }, { "text": "Influence of boundary conditions on level statistics and eigenstates at\n the metal insulator transition: We investigate the influence of the boundary conditions on the scale\ninvariant critical level statistics at the metal insulator transition of\ndisordered three-dimensional orthogonal and two-dimensional unitary and\nsymplectic tight-binding models. The distribution of the spacings between\nconsecutive eigenvalues is calculated numerically and shown to be different for\nperiodic and Dirichlet boundary conditions whereas the critical disorder\nremains unchanged. The peculiar correlations of the corresponding critical\neigenstates leading to anomalous diffusion seem not to be affected by the\nchange of the boundary conditions.", "category": "cond-mat_dis-nn" }, { "text": "Scaling Theory of Few-Particle Delocalization: We develop a scaling theory of interaction-induced delocalization of\nfew-particle states in disordered quantum systems. In the absence of\ninteractions, all single-particle states are localized in $d<3$, while in $d\n\\geq 3$ there is a critical disorder below which states are delocalized. We\nhypothesize that such a delocalization transition occurs for $n$-particle bound\nstates in $d$ dimensions when $d+n\\geq 4$. Exact calculations of\ndisorder-averaged $n$-particle Greens functions support our hypothesis. In\nparticular, we show that $3$-particle states in $d=1$ with nearest-neighbor\nrepulsion will delocalize with $W_c \\approx 1.4t$ and with localization length\ncritical exponent $\\nu = 1.5 \\pm 0.3$. The delocalization transition can be\nunderstood by means of a mapping onto a non-interacting problem with symplectic\nsymmetry. We discuss the importance of this result for many-body\ndelocalization, and how few-body delocalization can be probed in cold atom\nexperiments.", "category": "cond-mat_dis-nn" }, { "text": "Water adsorption on amorphous silica surfaces: A Car-Parrinello\n simulation study: A combination of classical molecular dynamics (MD) and ab initio\nCar-Parrinello molecular dynamics (CPMD) simulations is used to investigate the\nadsorption of water on a free amorphous silica surface. From the classical MD\nSiO_2 configurations with a free surface are generated which are then used as\nstarting configurations for the CPMD.We study the reaction of a water molecule\nwith a two-membered ring at the temperature T=300K. We show that the result of\nthis reaction is the formation of two silanol groups on the surface. The\nactivation energy of the reaction is estimated and it is shown that the\nreaction is exothermic.", "category": "cond-mat_dis-nn" }, { "text": "A mesoscopic approach to subcritical fatigue crack growth: We investigate a model for fatigue crack growth in which damage accumulation\nis assumed to follow a power law of the local stress amplitude, a form which\ncan be generically justified on the grounds of the approximately self-similar\naspect of microcrack distributions. Our aim is to determine the relation\nbetween model ingredients and the Paris exponent governing subcritical\ncrack-growth dynamics at the macroscopic scale, starting from a single small\nnotch propagating along a fixed line. By a series of analytical and numerical\ncalculations, we show that, in the absence of disorder, there is a critical\ndamage-accumulation exponent $\\gamma$, namely $\\gamma_c=2$, separating two\ndistinct regimes of behavior for the Paris exponent $m$. For $\\gamma>\\gamma_c$,\nthe Paris exponent is shown to assume the value $m=\\gamma$, a result which\nproves robust against the separate introduction of various modifying\ningredients. Explicitly, we deal here with (i) the requirement of a minimum\nstress for damage to occur; (ii) the presence of disorder in local damage\nthresholds; (iii) the possibility of crack healing. On the other hand, in the\nregime $\\gamma<\\gamma_c$ the Paris exponent is seen to be sensitive to the\ndifferent ingredients added to the model, with rapid healing or a high minimum\nstress for damage leading to $m=2$ for all $\\gamma<\\gamma_c$, in contrast with\nthe linear dependence $m=6-2\\gamma$ observed for very long characteristic\nhealing times in the absence of a minimum stress for damage. Upon the\nintroduction of disorder on the local fatigue thresholds, which leads to the\npossible appearance of multiple cracks along the propagation line, the Paris\nexponent tends to $m\\approx 4$ for $\\gamma\\lesssim 2$, while retaining the\nbehavior $m=\\gamma$ for $\\gamma\\gtrsim 4$.", "category": "cond-mat_dis-nn" }, { "text": "Kinetic-growth self-avoiding walks on small-world networks: Kinetically-grown self-avoiding walks have been studied on Watts-Strogatz\nsmall-world networks, rewired from a two-dimensional square lattice. The\nmaximum length L of this kind of walks is limited in regular lattices by an\nattrition effect, which gives finite values for its mean value < L >. For\nrandom networks, this mean attrition length < L > scales as a power of the\nnetwork size, and diverges in the thermodynamic limit (large system size N).\nFor small-world networks, we find a behavior that interpolates between those\ncorresponding to regular lattices and randon networks, for rewiring probability\np ranging from 0 to 1. For p < 1, the mean self-intersection and attrition\nlength of kinetically-grown walks are finite. For p = 1, < L > grows with\nsystem size as N^{1/2}, diverging in the thermodynamic limit. In this limit and\nclose to p = 1, the mean attrition length diverges as (1-p)^{-4}. Results of\napproximate probabilistic calculations agree well with those derived from\nnumerical simulations.", "category": "cond-mat_dis-nn" }, { "text": "Critical behavior of the 2D Ising model with long-range correlated\n disorder: We study critical behavior of the diluted 2D Ising model in the presence of\ndisorder correlations which decay algebraically with distance as $\\sim r^{-a}$.\nMapping the problem onto 2D Dirac fermions with correlated disorder we\ncalculate the critical properties using renormalization group up to two-loop\norder. We show that beside the Gaussian fixed point the flow equations have a\nnon trivial fixed point which is stable for $0.9950$, numerical analyses of the mean first-passage time $\\tau$ on\nvarious fractal lattices show that the logarithmic scaling of $\\tau$ with the\ndistance $l$, $\\ln\\tau\\sim l^{\\psi}$, is a general rule, characterized by a new\ndynamical exponent $\\psi$ of the underlying lattice.", "category": "cond-mat_dis-nn" }, { "text": "Comment on \"Critical point scaling of Ising spin glasses in a magnetic\n field\" by J. Yeo and M.A. Moore: In a section of a recent publication, [J. Yeo and M.A. Moore, Phys. Rev. B\n91, 104432 (2015)], the authors discuss some of the arguments in the paper by\nParisi and Temesv\\'ari [Nuclear Physics B 858, 293 (2012)]. In this comment, it\nis shown how these arguments are misinterpreted, and the existence of the\nAlmeida-Thouless transition in the upper critical dimension 6 reasserted.", "category": "cond-mat_dis-nn" }, { "text": "Retrieval Phase Diagrams of Non-monotonic Hopfield Networks: We investigate the retrieval phase diagrams of an asynchronous\nfully-connected attractor network with non-monotonic transfer function by means\nof a mean-field approximation. We find for the noiseless zero-temperature case\nthat this non-monotonic Hopfield network can store more patterns than a network\nwith monotonic transfer function investigated by Amit et al. Properties of\nretrieval phase diagrams of non-monotonic networks agree with the results\nobtained by Nishimori and Opris who treated synchronous networks. We also\ninvestigate the optimal storage capacity of the non-monotonic Hopfield model\nwith state-dependent synaptic couplings introduced by Zertuche et el. We show\nthat the non-monotonic Hopfield model with state-dependent synapses stores more\npatterns than the conventional Hopfield model. Our formulation can be easily\nextended to a general transfer function.", "category": "cond-mat_dis-nn" }, { "text": "Localization in 2D Quantum percolation: Quantum site percolation as a limiting case of binary alloy is studied\nnumerically in 2D within the tight-binding model. We address the transport\nproperties in all regimes - ballistic, diffusive (metallic), localized and\ncrossover between the latter two. Special attention is given to the region\nclose to the conduction band center, but even there the Anderson localization\npersists, without signs of metal - insulator transition. We found standard\nlocalization for sufficiently large samples. For smaller systems, novel partial\nquantization of Landauer conductances, i. e. most values close to small\nintegers in arbitrary units is observed at band center. The crossover types of\nconductance distributions (outside the band center) are found to be similar to\nsystems with corrugated surfaces. Universal conductance fluctuations in\nmetallic regime are shown to approach the known, theoretically predicted value.\nThe resonances in localized regime are Pendry necklaces. We tested Pendry's\nconjecture on the probability of such rare conducting samples and it proved\nconsistent with our numerical results.", "category": "cond-mat_dis-nn" }, { "text": "Response to Comment on \"Super-universality in Anderson localization\"\n arXiv:2210.10539v2: This is response to the recent comment arXiv:2210.10539v2 by I. Burmistrov.", "category": "cond-mat_dis-nn" }, { "text": "Hysteresis and Avalanches in the Random Anisotropy Ising Model: The behaviour of the Random Anisotropy Ising model at T=0 under local\nrelaxation dynamics is studied. The model includes a dominant ferromagnetic\ninteraction and assumes an infinite anisotropy at each site along local\nanisotropy axes which are randomly aligned. Two different random distributions\nof anisotropy axes have been studied. Both are characterized by a parameter\nthat allows control of the degree of disorder in the system. By using numerical\nsimulations we analyze the hysteresis loop properties and characterize the\nstatistical distribution of avalanches occuring during the metastable evolution\nof the system driven by an external field. A disorder-induced critical point is\nfound in which the hysteresis loop changes from displaying a typical\nferromagnetic magnetization jump to a rather smooth loop exhibiting only tiny\navalanches. The critical point is characterized by a set of critical exponents,\nwhich are consistent with the universal values proposed from the study of other\nsimpler models.", "category": "cond-mat_dis-nn" }, { "text": "Water adsorption on amorphous silica surfaces: A Car-Parrinello\n simulation study: A combination of classical molecular dynamics (MD) and ab initio\nCar-Parrinello molecular dynamics (CPMD) simulations is used to investigate the\nadsorption of water on a free amorphous silica surface. From the classical MD\nSiO_2 configurations with a free surface are generated which are then used as\nstarting configurations for the CPMD.We study the reaction of a water molecule\nwith a two-membered ring at the temperature T=300K. We show that the result of\nthis reaction is the formation of two silanol groups on the surface. The\nactivation energy of the reaction is estimated and it is shown that the\nreaction is exothermic.", "category": "cond-mat_dis-nn" }, { "text": "The random Blume-Capel model on cubic lattice: first order inverse\n freezing in a 3D spin-glass system: We present a numerical study of the Blume-Capel model with quenched disorder\nin 3D. The phase diagram is characterized by spin-glass/paramagnet phase\ntransitions of both first and second order in the thermodynamic sense.\nNumerical simulations are performed using the Exchange-Monte Carlo algorithm,\nproviding clear evidence for inverse freezing. The main features at criticality\nand in the phase coexistence region are investigated. The whole inverse\nfreezing transition appears to be first order. The second order transition\nappears to be in the same universality class of the Edwards-Anderson model. The\nnature of the spin-glass phase is analyzed by means of the finite size scaling\nbehavior of the overlap distribution functions and the four-spins real-space\ncorrelation functions. Evidence for a replica symmetry breaking-like\norganization of states is provided.", "category": "cond-mat_dis-nn" }, { "text": "A ferromagnet with a glass transition: We introduce a finite-connectivity ferromagnetic model with a three-spin\ninteraction which has a crystalline (ferromagnetic) phase as well as a glass\nphase. The model is not frustrated, it has a ferromagnetic equilibrium phase at\nlow temperature which is not reached dynamically in a quench from the\nhigh-temperature phase. Instead it shows a glass transition which can be\nstudied in detail by a one step replica-symmetry broken calculation. This spin\nmodel exhibits the main properties of the structural glass transition at a\nsolvable mean-field level.", "category": "cond-mat_dis-nn" }, { "text": "Transmission-eigenchannel velocity and diffusion: The diffusion model is used to calculate the time-averaged flow of particles\nin stochastic media and the propagation of waves averaged over ensembles of\ndisordered static configurations. For classical waves exciting static\ndisordered samples, such as a layer of paint or a tissue sample, the flux\ntransmitted through the sample may be dramatically enhanced or suppressed\nrelative to predictions of diffusion theory when the sample is excited by a\nwaveform corresponding to a transmission eigenchannel. Even so, it is widely\nacknowledged that the velocity of waves is irretrievably randomized in\nscattering media. Here we demonstrate in microwave measurements and numerical\nsimulations that the statistics of velocity of different transmission\neigenchannels remain distinct on all length scales and are identical on the\nincident and output surfaces. The interplay between eigenchannel velocities and\ntransmission eigenvalues determines the energy density within the medium, the\ndiffusion coefficient, and the dynamics of propagation. the diffusion\ncoefficient and all scatter9ng parameters, including the scattering mean free\npath, oscillate with width of the sample as the number and shape of the\npropagating channels in the medium change.", "category": "cond-mat_dis-nn" }, { "text": "Improved field theoretical approach to noninteracting Brownian particles\n in a quenched random potential: We construct a dynamical field theory for noninteracting Brownian particles\nin the presence of a quenched Gaussian random potential. The main variable for\nthe field theory is the density fluctuation which measures the difference\nbetween the local density and its average value. The average density is\nspatially inhomogeneous for given realization of the random potential. It\nbecomes uniform only after averaged over the disorder configurations. We\ndevelop the diagrammatic perturbation theory for the density correlation\nfunction and calculate the zero-frequency component of the response function\nexactly by summing all the diagrams contributing to it. From this exact result\nand the fluctuation dissipation relation, which holds in an equilibrium\ndynamics, we find that the connected density correlation function always decays\nto zero in the long-time limit for all values of disorder strength implying\nthat the system always remains ergodic. This nonperturbative calculation relies\non the simple diagrammatic structure of the present field theoretical scheme.\nWe compare in detail our diagrammatic perturbation theory with the one used in\na recent paper [B.\\ Kim, M.\\ Fuchs and V.\\ Krakoviack, J.\\ Stat.\\ Mech.\\ (2020)\n023301], which uses the density fluctuation around the uniform average, and\ndiscuss the difference in the diagrammatic structures of the two formulations.", "category": "cond-mat_dis-nn" }, { "text": "Sherrington-Kirkpatrick model near $T=T_c$: expanding around the Replica\n Symmetric Solution: An expansion for the free energy functional of the Sherrington-Kirkpatrick\n(SK) model, around the Replica Symmetric SK solution $Q^{({\\rm RS})}_{ab} =\n\\delta_{ab} + q(1-\\delta_{ab})$ is investigated. In particular, when the\nexpansion is truncated to fourth order in. $Q_{ab} - Q^{({\\rm RS})}_{ab}$. The\nFull Replica Symmetry Broken (FRSB) solution is explicitly found but it turns\nout to exist only in the range of temperature $0.549...\\leq T\\leq T_c=1$, not\nincluding T=0. On the other hand an expansion around the paramagnetic solution\n$Q^{({\\rm PM})}_{ab} = \\delta_{ab}$ up to fourth order yields a FRSB solution\nthat exists in a limited temperature range $0.915...\\leq T \\leq T_c=1$.", "category": "cond-mat_dis-nn" }, { "text": "Percolation and jamming in random sequential adsorption of linear\n segments on square lattice: We present the results of study of random sequential adsorption of linear\nsegments (needles) on sites of a square lattice. We show that the percolation\nthreshold is a nonmonotonic function of the length of the adsorbed needle,\nshowing a minimum for a certain length of the needles, while the jamming\nthreshold decreases to a constant with a power law. The ratio of the two\nthresholds is also nonmonotonic and it remains constant only in a restricted\nrange of the needles length. We determine the values of the correlation length\nexponent for percolation, jamming and their ratio.", "category": "cond-mat_dis-nn" }, { "text": "Strongly disordered spin ladders: The effect of quenched disorder on the low-energy properties of various\nantiferromagnetic spin ladder models is studied by a numerical strong disorder\nrenormalization group method and by density matrix renormalization. For strong\nenough disorder the originally gapped phases with finite topological or dimer\norder become gapless. In these quantum Griffiths phases the scaling of the\nenergy, as well as the singularities in the dynamical quantities are\ncharacterized by a finite dynamical exponent, z, which varies with the strength\nof disorder. At the phase boundaries, separating topologically distinct\nGriffiths phases the singular behavior of the disordered ladders is generally\ncontrolled by an infinite randomness fixed point.", "category": "cond-mat_dis-nn" }, { "text": "Hierarchical neural networks perform both serial and parallel processing: In this work we study a Hebbian neural network, where neurons are arranged\naccording to a hierarchical architecture such that their couplings scale with\ntheir reciprocal distance. As a full statistical mechanics solution is not yet\navailable, after a streamlined introduction to the state of the art via that\nroute, the problem is consistently approached through signal- to-noise\ntechnique and extensive numerical simulations. Focusing on the low-storage\nregime, where the amount of stored patterns grows at most logarithmical with\nthe system size, we prove that these non-mean-field Hopfield-like networks\ndisplay a richer phase diagram than their classical counterparts. In\nparticular, these networks are able to perform serial processing (i.e. retrieve\none pattern at a time through a complete rearrangement of the whole ensemble of\nneurons) as well as parallel processing (i.e. retrieve several patterns\nsimultaneously, delegating the management of diff erent patterns to diverse\ncommunities that build network). The tune between the two regimes is given by\nthe rate of the coupling decay and by the level of noise affecting the system.\nThe price to pay for those remarkable capabilities lies in a network's capacity\nsmaller than the mean field counterpart, thus yielding a new budget principle:\nthe wider the multitasking capabilities, the lower the network load and\nviceversa. This may have important implications in our understanding of\nbiological complexity.", "category": "cond-mat_dis-nn" }, { "text": "Quantum-Mechanically Induced Asymmetry in the Phase Diagrams of\n Spin-Glass Systems: The spin-1/2 quantum Heisenberg model is studied in all spatial dimensions d\nby renormalization-group theory. Strongly asymmetric phase diagrams in\ntemperature and antiferromagnetic bond probability p are obtained in dimensions\nd \\geq 3. The asymmetry at high temperatures approaching the pure ferromagnetic\nand antiferromagnetic systems disappears as d is increased. However, the\nasymmetry at low but finite temperatures remains in all dimensions, with the\nantiferromagnetic phase receding to the ferromagnetic phase. A\nfinite-temperature second-order phase boundary directly between the\nferromagnetic and antiferromagnetic phases occurs in d \\geq 6, resulting in a\nnew multicritical point at its meeting with the boundaries to the paramagnetic\nphase. In d=3,4,5, a paramagnetic phase reaching zero temperature intervenes\nasymmetrically between the ferromagnetic and reentrant antiferromagnetic\nphases. There is no spin-glass phase in any dimension.", "category": "cond-mat_dis-nn" }, { "text": "Real Space Renormalization Group Theory of Disordered Models of Glasses: We develop a real space renormalisation group analysis of disordered models\nof glasses, in particular of the spin models at the origin of the Random First\nOrder Transition theory. We find three fixed points respectively associated to\nthe liquid state, to the critical behavior and to the glass state. The latter\ntwo are zero-temperature ones; this provides a natural explanation of the\ngrowth of effective activation energy scale and the concomitant huge increase\nof relaxation time approaching the glass transition. The lower critical\ndimension depends on the nature of the interacting degrees of freedom and is\nhigher than three for all models. This does not prevent three dimensional\nsystems from being glassy. Indeed, we find that their renormalisation group\nflow is affected by the fixed points existing in higher dimension and in\nconsequence is non-trivial. Within our theoretical framework the glass\ntransition results to be an avoided phase transition.", "category": "cond-mat_dis-nn" }, { "text": "Thermal conductance of one dimensional disordered harmonic chains: We study heat conduction mediated by longitudinal phonons in one dimensional\ndisordered harmonic chains. Using scaling properties of the phonon density of\nstates and localization in disordered systems, we find non-trivial scaling of\nthe thermal conductance with the system size. Our findings are corroborated by\nextensive numerical analysis. We show that a system with strong disorder,\ncharacterized by a `heavy-tailed' probability distribution, and with large\nimpedance mismatch between the bath and the system satisfies Fourier's law. We\nidentify a dimensionless scaling parameter, related to the temperature scale\nand the localization length of the phonons, through which the thermal\nconductance for different models of disorder and different temperatures follows\na universal behavior.", "category": "cond-mat_dis-nn" }, { "text": "Quantitative analysis of a Schaffer collateral model: Advances in techniques for the formal analysis of neural networks have\nintroduced the possibility of detailed quantitative analyses of brain\ncircuitry. This paper applies a method for calculating mutual information to\nthe analysis of the Schaffer collateral connections between regions CA3 and CA1\nof the hippocampus. Attention is given to the introduction of further details\nof anatomy and physiology to the calculation: in particular, the distribution\nof the number of connections that CA1 neurons receive from CA3, and the graded\nnature of the firing-rate distribution in region CA3.", "category": "cond-mat_dis-nn" }, { "text": "Hexatic-Herringbone Coupling at the Hexatic Transition in Smectic Liquid\n Crystals: 4-$\u03b5$ Renormalization Group Calculations Revisited: Simple symmetry considerations would suggest that the transition from the\nsmectic-A phase to the long-range bond orientationally ordered hexatic\nsmectic-B phase should belong to the XY universality class. However, a number\nof experimental studies have constantly reported over the past twenty years\n\"novel\" critical behavior with non-XY critical exponents for this transition.\nBruinsma and Aeppli argued in Physical Review Letters {\\bf 48}, 1625 (1982),\nusing a $4-\\epsilon$ renormalization-group calculation, that short-range\nmolecular herringbone correlations coupled to the hexatic ordering drive this\ntransition first order via thermal fluctuations, and that the critical behavior\nobserved in real systems is controlled by a `nearby' tricritical point. We have\nrevisited the model of Bruinsma and Aeppli and present here the results of our\nstudy. We have found two nontrivial strongly-coupled herringbone-hexatic fixed\npoints apparently missed by those authors. Yet, those two new nontrivial\nfixed-points are unstable, and we obtain the same final conclusion as the one\nreached by Bruinsma and Aeppli, namely that of a fluctuation-driven first order\ntransition. We also discuss the effect of local two-fold distortion of the bond\norder as a possible missing order parameter in the Hamiltonian.", "category": "cond-mat_dis-nn" }, { "text": "Topological properties of hierarchical networks: Hierarchical networks are attracting a renewal interest for modelling the\norganization of a number of biological systems and for tackling the complexity\nof statistical mechanical models beyond mean-field limitations. Here we\nconsider the Dyson hierarchical construction for ferromagnets, neural networks\nand spin-glasses, recently analyzed from a statistical-mechanics perspective,\nand we focus on the topological properties of the underlying structures. In\nparticular, we find that such structures are weighted graphs that exhibit high\ndegree of clustering and of modularity, with small spectral gap; the robustness\nof such features with respect to link removal is also studied. These outcomes\nare then discussed and related to the statistical mechanics scenario in full\nconsistency. Lastly, we look at these weighted graphs as Markov chains and we\nshow that in the limit of infinite size, the emergence of ergodicity breakdown\nfor the stochastic process mirrors the emergence of meta-stabilities in the\ncorresponding statistical mechanical analysis.", "category": "cond-mat_dis-nn" }, { "text": "Statistics of anomalously localized states at the center of band E=0 in\n the one-dimensional Anderson localization model: We consider the distribution function $P(|\\psi|^{2})$ of the eigenfunction\namplitude at the center-of-band (E=0) anomaly in the one-dimensional\ntight-binding chain with weak uncorrelated on-site disorder (the\none-dimensional Anderson model). The special emphasis is on the probability of\nthe anomalously localized states (ALS) with $|\\psi|^{2}$ much larger than the\ninverse typical localization length $\\ell_{0}$. Using the solution to the\ngenerating function $\\Phi_{an}(u,\\phi)$ found recently in our works we find the\nALS probability distribution $P(|\\psi|^{2})$ at $|\\psi|^{2}\\ell_{0} >> 1$. As\nan auxiliary preliminary step we found the asymptotic form of the generating\nfunction $\\Phi_{an}(u,\\phi)$ at $u >> 1$ which can be used to compute other\nstatistical properties at the center-of-band anomaly. We show that at\nmoderately large values of $|\\psi|^{2}\\ell_{0}$, the probability of ALS at E=0\nis smaller than at energies away from the anomaly. However, at very large\nvalues of $|\\psi|^{2}\\ell_{0}$, the tendency is inverted: it is exponentially\neasier to create a very strongly localized state at E=0 than at energies away\nfrom the anomaly. We also found the leading term in the behavior of\n$P(|\\psi|^{2})$ at small $|\\psi|^{2}<< \\ell_{0}^{-1}$ and show that it is\nconsistent with the exponential localization corresponding to the Lyapunov\nexponent found earlier by Kappus and Wegner and Derrida and Gardner.", "category": "cond-mat_dis-nn" }, { "text": "Anderson localization of one-dimensional hybrid particles: We solve the Anderson localization problem on a two-leg ladder by the\nFokker-Planck equation approach. The solution is exact in the weak disorder\nlimit at a fixed inter-chain coupling. The study is motivated by progress in\ninvestigating the hybrid particles such as cavity polaritons. This application\ncorresponds to parametrically different intra-chain hopping integrals (a \"fast\"\nchain coupled to a \"slow\" chain). We show that the canonical\nDorokhov-Mello-Pereyra-Kumar (DMPK) equation is insufficient for this problem.\nIndeed, the angular variables describing the eigenvectors of the transmission\nmatrix enter into an extended DMPK equation in a non-trivial way, being\nentangled with the two transmission eigenvalues. This extended DMPK equation is\nsolved analytically and the two Lyapunov exponents are obtained as functions of\nthe parameters of the disordered ladder. The main result of the paper is that\nnear the resonance energy, where the dispersion curves of the two decoupled and\ndisorder-free chains intersect, the localization properties of the ladder are\ndominated by those of the slow chain. Away from the resonance they are\ndominated by the fast chain: a local excitation on the slow chain may travel a\ndistance of the order of the localization length of the fast chain.", "category": "cond-mat_dis-nn" }, { "text": "Routes towards Anderson-Like localization of Bose-Einstein condensates\n in disordered optical lattices: We investigate, both experimentally and theoretically, possible routes\ntowards Anderson-like localization of Bose-Einstein condensates in disordered\npotentials. The dependence of this quantum interference effect on the nonlinear\ninteractions and the shape of the disorder potential is investigated.\nExperiments with an optical lattice and a superimposed disordered potential\nreveal the lack of Anderson localization. A theoretical analysis shows that\nthis absence is due to the large length scale of the disorder potential as well\nas its screening by the nonlinear interactions. Further analysis shows that\nincommensurable superlattices should allow for the observation of the\ncross-over from the nonlinear screening regime to the Anderson localized case\nwithin realistic experimental parameters.", "category": "cond-mat_dis-nn" }, { "text": "Slow Dynamics in a Two-Dimensional Anderson-Hubbard Model: We study the real-time dynamics of a two-dimensional Anderson--Hubbard model\nusing nonequilibrium self-consistent perturbation theory within the second-Born\napproximation. When compared with exact diagonalization performed on small\nclusters, we demonstrate that for strong disorder this technique approaches the\nexact result on all available timescales, while for intermediate disorder, in\nthe vicinity of the many-body localization transition, it produces\nquantitatively accurate results up to nontrivial times. Our method allows for\nthe treatment of system sizes inaccessible by any numerically exact method and\nfor the complete elimination of finite size effects for the times considered.\nWe show that for a sufficiently strong disorder the system becomes nonergodic,\nwhile for intermediate disorder strengths and for all accessible time scales\ntransport in the system is strictly subdiffusive. We argue that these results\nare incompatible with a simple percolation picture, but are consistent with the\nheuristic random resistor network model where subdiffusion may be observed for\nlong times until a crossover to diffusion occurs. The prediction of slow\nfinite-time dynamics in a two-dimensional interacting and disordered system can\nbe directly verified in future cold atoms experiments", "category": "cond-mat_dis-nn" }, { "text": "Ideal quantum glass transitions: many-body localization without quenched\n disorder: We explore the possibility for translationally invariant quantum many-body\nsystems to undergo a dynamical glass transition, at which ergodicity and\ntranslational invariance break down spontaneously, driven entirely by quantum\neffects. In contrast to analogous classical systems, where the existence of\nsuch an ideal glass transition remains a controversial issue, a genuine phase\ntransition is predicted in the quantum regime. This ideal quantum glass\ntransition can be regarded as a many-body localization transition due to\nself-generated disorder. Despite their lack of thermalization, these\ndisorder-free quantum glasses do not possess an extensive set of local\nconserved operators, unlike what is conjectured for many-body localized systems\nwith strong quenched disorder.", "category": "cond-mat_dis-nn" }, { "text": "Origin of the Growing Length Scale in M-p-Spin Glass Models: Two versions of the M-p-spin glass model have been studied with the\nMigdal-Kadanoff renormalization group approximation. The model with p=3 and M=3\nhas at mean-field level the ideal glass transition at the Kauzmann temperature\nand at lower temperatures still the Gardner transition to a state like that of\nan Ising spin glass in a field. The model with p=3 and M=2 has only the Gardner\ntransition. In the dimensions studied, d=2,3 and 4, both models behave almost\nidentically, indicating that the growing correlation length as the temperature\nis reduced in these models -- the analogue of the point-to-set length scale --\nis not due to the mechanism postulated in the random first order transition\ntheory of glasses, but is more like that expected on the analogy of glasses to\nthe Ising spin glass in a field.", "category": "cond-mat_dis-nn" }, { "text": "Absence of the diffusion pole in the Anderson insulator: We discuss conditions for the existence of the diffusion pole and its\nconsequences in disordered noninteracting electron systems. Using only\nnonperturbative and exact arguments we find against expectations that the\ndiffusion pole can exist only in the diffusive (metallic) regime. We\ndemonstrate that the diffusion pole in the Anderson localization phase would\nlead to nonexistence of the self-energy and hence to a physically inconsistent\npicture. The way how to consistently treat and understand the Anderson\nlocalization transition with vanishing of the diffusion pole is presented.", "category": "cond-mat_dis-nn" }, { "text": "Scaling Law and Aging Phenomena in the Random Energy Model: We study the effect of temperature shift on aging phenomena in the Random\nEnergy Model (REM). From calculation on the correlation function and simulation\non the Zero-Field-Cooled magnetization, we find that the REM satisfies a\nscaling relation even if temperature is shifted. Furthermore, this scaling\nproperty naturally leads to results obtained in experiment and the droplet\ntheory.", "category": "cond-mat_dis-nn" }, { "text": "Many-body localization of ${\\mathbb Z}_3$ Fock parafermions: We study the effects of a random magnetic field on a one-dimensional (1D)\nspin-1 chain with {\\it correlated} nearest-neighbor $XY$ interaction. We show\nthat this spin model can be exactly mapped onto the 1D disordered tight-binding\nmodel of ${\\mathbb Z}_3$ Fock parafermions (FPFs), exotic anyonic\nquasiparticles that generalize usual spinless fermions. Thus, we have a\npeculiar case of a disordered Hamiltonian that, despite being bilinear in the\ncreation and annihilation operators, exhibits a many-body localization (MBL)\ntransition owing to the nontrivial statistics of FPFs. This is in sharp\ncontrast to conventional bosonic and fermionic quadratic disordered\nHamiltonians that show single-particle (Anderson) localization. We perform\nfinite-size exact diagonalization calculations of level-spacing statistics,\nfractal dimensions, and entanglement entropy, and provide convincing evidence\nfor the MBL transition at finite disorder strength.", "category": "cond-mat_dis-nn" }, { "text": "Topological phases of amorphous matter: Topological phases of matter are often understood and predicted with the help\nof crystal symmetries, although they don't rely on them to exist. In this\nchapter we review how topological phases have been recently shown to emerge in\namorphous systems. We summarize the properties of topological states and\ndiscuss how disposing of translational invariance has motivated the surge of\nnew tools to characterize topological states in amorphous systems, both\ntheoretically and experimentally. The ubiquity of amorphous systems combined\nwith the robustness of topology has the potential to bring new fundamental\nunderstanding in our classification of phases of matter, and inspire new\ntechnological developments.", "category": "cond-mat_dis-nn" }, { "text": "Conductance distribution in 1D systems: dependence on the Fermi level\n and the ideal leads: The correct definition of the conductance of finite systems implies a\nconnection to the system of the massive ideal leads. Influence of the latter on\nthe properties of the system appears to be rather essential and is studied\nbelow on the simplest example of the 1D case. In the log-normal regime this\ninfluence is reduced to the change of the absolute scale of conductance, but\ngenerally changes the whole distribution function. Under the change of the\nsystem length L, its resistance may undergo the periodic or aperiodic\noscillations. Variation of the Fermi level induces qualitative changes in the\nconductance distribution, resembling the smoothed Anderson transition.", "category": "cond-mat_dis-nn" }, { "text": "Spin glass behavior in a random Coulomb antiferromagnet: We study spin glass behavior in a random Ising Coulomb antiferromagnet in two\nand three dimensions using Monte Carlo simulations. In two dimensions, we find\na transition at zero temperature with critical exponents consistent with those\nof the Edwards Anderson model, though with large uncertainties. In three\ndimensions, evidence for a finite-temperature transition, as occurs in the\nEdwards-Anderson model, is rather weak. This may indicate that the sizes are\ntoo small to probe the asymptotic critical behavior, or possibly that the\nuniversality class is different from that of the Edwards-Anderson model and has\na lower critical dimension equal to three.", "category": "cond-mat_dis-nn" }, { "text": "Laplacian Coarse Graining in Complex Networks: Complex networks can model a range of different systems, from the human brain\nto social connections. Some of those networks have a large number of nodes and\nlinks, making it impractical to analyze them directly. One strategy to simplify\nthese systems is by creating miniaturized versions of the networks that keep\ntheir main properties. A convenient tool that applies that strategy is the\nrenormalization group (RG), a methodology used in statistical physics to change\nthe scales of physical systems. This method consists of two steps: a coarse\ngrain, where one reduces the size of the system, and a rescaling of the\ninteractions to compensate for the information loss. This work applies RG to\ncomplex networks by introducing a coarse-graining method based on the Laplacian\nmatrix. We use a field-theoretical approach to calculate the correlation\nfunction and coarse-grain the most correlated nodes into super-nodes, applying\nour method to several artificial and real-world networks. The results are\npromising, with most of the networks under analysis showing self-similar\nproperties across different scales.", "category": "cond-mat_dis-nn" }, { "text": "Spatial correlations in the relaxation of the Kob-Andersen model: We describe spatio-temporal correlations and heterogeneities in a kinetically\nconstrained glassy model, the Kob-Andersen model. The kinetic constraints of\nthe model alone induce the existence of dynamic correlation lengths, that\nincrease as the density $\\rho$ increases, in a way compatible with a\ndouble-exponential law. We characterize in detail the trapping time correlation\nlength, the cooperativity length, and the distribution of persistent clusters\nof particles. This last quantity is related to the typical size of blocked\nclusters that slow down the dynamics for a given density.", "category": "cond-mat_dis-nn" }, { "text": "TASEP Exit Times: We address the question of the time needed by $N$ particles, initially\nlocated on the first sites of a finite 1D lattice of size $L$, to exit that\nlattice when they move according to a TASEP transport model. Using analytical\ncalculations and numerical simulations, we show that when $N \\ll L$, the mean\nexit time of the particles is asymptotically given by $T_N(L) \\sim L+\\beta_N\n\\sqrt{L}$ for large lattices. Building upon exact results obtained for 2\nparticles, we devise an approximate continuous space and time description of\nthe random motion of the particles that provides an analytical recursive\nrelation for the coefficients $\\beta_N$. The results are shown to be in very\ngood agreement with numerical results. This approach sheds some light on the\nexit dynamics of $N$ particles in the regime where $N$ is finite while the\nlattice size $L\\rightarrow \\infty$. This complements previous asymptotic\nresults obtained by Johansson in \\cite{Johansson2000} in the limit where both\n$N$ and $L$ tend to infinity while keeping the particle density $N/L$ finite.", "category": "cond-mat_dis-nn" }, { "text": "Out of equilibrium Phase Diagram of the Quantum Random Energy Model: In this paper we study the out-of-equilibrium phase diagram of the quantum\nversion of Derrida's Random Energy Model, which is the simplest model of\nmean-field spin glasses. We interpret its corresponding quantum dynamics in\nFock space as a one-particle problem in very high dimension to which we apply\ndifferent theoretical methods tailored for high-dimensional lattices: the\nForward-Scattering Approximation, a mapping to the Rosenzweig-Porter model, and\nthe cavity method. Our results indicate the existence of two transition lines\nand three distinct dynamical phases: a completely many-body localized phase at\nlow energy, a fully ergodic phase at high energy, and a multifractal \"bad\nmetal\" phase at intermediate energy. In the latter, eigenfunctions occupy a\ndiverging volume, yet an exponentially vanishing fraction of the total Hilbert\nspace. We discuss the limitations of our approximations and the relationship\nwith previous studies.", "category": "cond-mat_dis-nn" }, { "text": "Hysteresis, Avalanches, and Noise: Numerical Methods: In studying the avalanches and noise in a model of hysteresis loops we have\ndeveloped two relatively straightforward algorithms which have allowed us to\nstudy large systems efficiently. Our model is the random-field Ising model at\nzero temperature, with deterministic albeit random dynamics. The first\nalgorithm, implemented using sorted lists, scales in computer time as O(N log\nN), and asymptotically uses N (sizeof(double)+ sizeof(int)) bits of memory. The\nsecond algorithm, which never generates the random fields, scales in time as\nO(N \\log N) and asymptotically needs storage of only one bit per spin, about 96\ntimes less memory than the first algorithm. We present results for system sizes\nof up to a billion spins, which can be run on a workstation with 128MB of RAM\nin a few hours. We also show that important physical questions were resolved\nonly with the largest of these simulations.", "category": "cond-mat_dis-nn" }, { "text": "Antagonistic interactions can stabilise fixed points in heterogeneous\n linear dynamical systems: We analyse the stability of large, linear dynamical systems of variables that\ninteract through a fully connected random matrix and have inhomogeneous growth\nrates. We show that in the absence of correlations between the coupling\nstrengths, a system with interactions is always less stable than a system\nwithout interactions. Contrarily to the uncorrelated case, interactions that\nare antagonistic, i.e., characterised by negative correlations, can stabilise\nlinear dynamical systems. In particular, when the strength of the interactions\nis not too strong, systems with antagonistic interactions are more stable than\nsystems without interactions. These results are obtained with an exact theory\nfor the spectral properties of fully connected random matrices with diagonal\ndisorder.", "category": "cond-mat_dis-nn" }, { "text": "Navigating Networks with Limited Information: We study navigation with limited information in networks and demonstrate that\nmany real-world networks have a structure which can be described as favoring\ncommunication at short distance at the cost of constraining communication at\nlong distance. This feature, which is robust and more evident with limited than\nwith complete information, reflects both topological and possibly functional\ndesign characteristics. For example, the characteristics of the networks\nstudied derived from a city and from the Internet are manifested through\nmodular network designs. We also observe that directed navigation in typical\nnetworks requires remarkably little information on the level of individual\nnodes. By studying navigation, or specific signaling, we take a complementary\napproach to the common studies of information transfer devoted to broadcasting\nof information in studies of virus spreading and the like.", "category": "cond-mat_dis-nn" }, { "text": "Systematic Series Expansions for Processes on Networks: We use series expansions to study dynamics of equilibrium and non-equilibrium\nsystems on networks. This analytical method enables us to include detailed\nnon-universal effects of the network structure. We show that even low order\ncalculations produce results which compare accurately to numerical simulation,\nwhile the results can be systematically improved. We show that certain commonly\naccepted analytical results for the critical point on networks with a broad\ndegree distribution need to be modified in certain cases due to\ndisassortativity; the present method is able to take into account the\nassortativity at sufficiently high order, while previous results correspond to\nleading and second order approximations in this method. Finally, we apply this\nmethod to real-world data.", "category": "cond-mat_dis-nn" }, { "text": "Interface fluctuations in disordered systems: Universality and\n non-Gaussian statistics: We employ a functional renormalization group to study interfaces in the\npresence of a pinning potential in $d=4-\\epsilon$ dimensions. In contrast to a\nprevious approach [D.S. Fisher, Phys. Rev. Lett. {\\bf 56}, 1964 (1986)] we use\na soft-cutoff scheme. With the method developed here we confirm the value of\nthe roughness exponent $\\zeta \\approx 0.2083 \\epsilon$ in order $\\epsilon$.\nGoing beyond previous work, we demonstrate that this exponent is universal. In\naddition, we analyze the generation of higher cumulants in the disorder\ndistribution and the role of temperature as a dangerously irrelevant variable.", "category": "cond-mat_dis-nn" }, { "text": "Dynamic Gardner crossover in a simple structural glass: The criticality of the jamming transition responsible for amorphous\nsolidification has been theoretically linked to the marginal stability of a\nthermodynamic Gardner phase. While the critical exponents of jamming appear\nindependent of the preparation history, the pertinence of Gardner physics far\nfrom equilibrium is an open question. To fill this gap, we numerically study\nthe nonequilibrium dynamics of hard disks compressed towards the jamming\ntransition using a broad variety of protocols. We show that dynamic signatures\nof Gardner physics can be disentangled from the aging relaxation dynamics. We\nthus define a generic dynamic Gardner crossover regardless of the history. Our\nresults show that the jamming transition is always accessed by exploring\nincreasingly complex landscape, resulting in the anomalous microscopic\nrelaxation dynamics that remains to be understood theoretically.", "category": "cond-mat_dis-nn" }, { "text": "Optical response of electrons in a random potential: Using our recently developed Chebyshev expansion technique for\nfinite-temperature dynamical correlation functions we numerically study the AC\nconductivity $\\sigma(\\omega)$ of the Anderson model on large cubic clusters of\nup to $100^3$ sites. Extending previous results we focus on the role of the\nboundary conditions and check the consistency of the DC limit, $\\omega\\to 0$,\nby comparing with direct conductance calculations based on a Greens function\napproach in a Landauer B\\\"uttiker type setup.", "category": "cond-mat_dis-nn" }, { "text": "Free energy landscapes, dynamics and the edge of chaos in mean-field\n models of spin glasses: Metastable states in Ising spin-glass models are studied by finding iterative\nsolutions of mean-field equations for the local magnetizations. Two different\nequations are studied: the TAP equations which are exact for the SK model, and\nthe simpler `naive-mean-field' (NMF) equations. The free-energy landscapes that\nemerge are very different. For the TAP equations, the numerical studies confirm\nthe analytical results of Aspelmeier et al., which predict that TAP states\nconsist of close pairs of minima and index-one (one unstable direction) saddle\npoints, while for the NMF equations saddle points with large indices are found.\nFor TAP the barrier height between a minimum and its nearby saddle point scales\nas (f-f_0)^{-1/3} where f is the free energy per spin of the solution and f_0\nis the equilibrium free energy per spin. This means that for `pure states', for\nwhich f-f_0 is of order 1/N, the barriers scale as N^{1/3}, but between states\nfor which f-f_0 is of order one the barriers are finite and also small so such\nmetastable states will be of limited physical significance. For the NMF\nequations there are saddles of index K and we can demonstrate that their\ncomplexity Sigma_K scales as a function of K/N. We have also employed an\niterative scheme with a free parameter that can be adjusted to bring the system\nof equations close to the `edge of chaos'. Both for the TAP and NME equations\nit is possible with this approach to find metastable states whose free energy\nper spin is close to f_0. As N increases, it becomes harder and harder to find\nsolutions near the edge of chaos, but nevertheless the results which can be\nobtained are competitive with those achieved by more time-consuming computing\nmethods and suggest that this method may be of general utility.", "category": "cond-mat_dis-nn" }, { "text": "Modular synchronization in complex networks with a gauge Kuramoto model: We modify the Kuramoto model for synchronization on complex networks by\nintroducing a gauge term that depends on the edge betweenness centrality (BC).\nThe gauge term introduces additional phase difference between two vertices from\n0 to $\\pi$ as the BC on the edge between them increases from the minimum to the\nmaximum in the network. When the network has a modular structure, the model\ngenerates the phase synchronization within each module, however, not over the\nentire system. Based on this feature, we can distinguish modules in complex\nnetworks, with relatively little computational time of $\\mathcal{O}(NL)$, where\n$N$ and $L$ are the number of vertices and edges in the system, respectively.\nWe also examine the synchronization of the modified Kuramoto model and compare\nit with that of the original Kuramoto model in several complex networks.", "category": "cond-mat_dis-nn" }, { "text": "Statistics of Resonances and Delay Times in Random Media: Beyond Random\n Matrix Theory: We review recent developments on quantum scattering from mesoscopic systems.\nVarious spatial geometries whose closed analogs shows diffusive, localized or\ncritical behavior are considered. These are features that cannot be described\nby the universal Random Matrix Theory results. Instead one has to go beyond\nthis approximation and incorporate them in a non-perturbative way. Here, we pay\nparticular emphasis to the traces of these non-universal characteristics, in\nthe distribution of the Wigner delay times and resonance widths. The former\nquantity captures time dependent aspects of quantum scattering while the latter\nis associated with the poles of the scattering matrix.", "category": "cond-mat_dis-nn" }, { "text": "Interplay and competition between disorder and flat band in an\n interacting Creutz ladder: We clarify the interplay and competition between disorder and flat band in\nthe Creutz ladder with inter-particle interactions focusing on the system's\ndynamics. Without disorder, the Creutz ladder exhibits flat-band many-body\nlocalization (FMBL). In this work, we find that disorder generates drastic\neffects on the system, i.e., addition of it induces a thermal phase first and\nfurther increase of it leads the system to the conventional many-body-localized\n(MBL) phase. The competition gives novel localization properties and\nunconventional quench dynamics to the system. We first draw the global sketch\nof the localization phase diagram by focusing on the two-particle system. The\nthermal phase intrudes between the FMBL and MBL phases, the regime of which\ndepends on the strength of disorder and interactions. Based on the two-particle\nphase diagram and the properties of the quench dynamics, we further investigate\nfinite-filling cases in detail. At finite-filling fractions, we again find that\nthe interplay/competition between the interactions and disorder in the original\nflat-band Creutz ladder induces thermal phase, which separates the FMBL and MBL\nphases. We also verify that the time evolution of the system coincides with the\nstatic phase diagrams. For suitable fillings, the conservation of the\ninitial-state information and low-growth entanglement dynamics are also\nobserved. These properties depend on the strength of disorder and interactions.", "category": "cond-mat_dis-nn" }, { "text": "Instantons in the working memory: implications for schizophrenia: The influence of the synaptic channel properties on the stability of delayed\nactivity maintained by recurrent neural network is studied. The duration of\nexcitatory post-synaptic current (EPSC) is shown to be essential for the global\nstability of the delayed response. NMDA receptor channel is a much more\nreliable mediator of the reverberating activity than AMPA receptor, due to a\nlonger EPSC. This allows to interpret the deterioration of working memory\nobserved in the NMDA channel blockade experiments. The key mechanism leading to\nthe decay of the delayed activity originates in the unreliability of the\nsynaptic transmission. The optimum fluctuation of the synaptic conductances\nleading to the decay is identified. The decay time is calculated analytically\nand the result is confirmed computationally.", "category": "cond-mat_dis-nn" }, { "text": "Criticality and entanglement in random quantum systems: We review studies of entanglement entropy in systems with quenched\nrandomness, concentrating on universal behavior at strongly random quantum\ncritical points. The disorder-averaged entanglement entropy provides insight\ninto the quantum criticality of these systems and an understanding of their\nrelationship to non-random (\"pure\") quantum criticality. The entanglement near\nmany such critical points in one dimension shows a logarithmic divergence in\nsubsystem size, similar to that in the pure case but with a different universal\ncoefficient. Such universal coefficients are examples of universal critical\namplitudes in a random system. Possible measurements are reviewed along with\nthe one-particle entanglement scaling at certain Anderson localization\ntransitions. We also comment briefly on higher dimensions and challenges for\nthe future.", "category": "cond-mat_dis-nn" }, { "text": "Gauged Neural Network: Phase Structure, Learning, and Associative Memory: A gauge model of neural network is introduced, which resembles the Z(2) Higgs\nlattice gauge theory of high-energy physics. It contains a neuron variable $S_x\n= \\pm 1$ on each site $x$ of a 3D lattice and a synaptic-connection variable\n$J_{x\\mu} = \\pm 1$ on each link $(x,x+\\hat{\\mu}) (\\mu=1,2,3)$. The model is\nregarded as a generalization of the Hopfield model of associative memory to a\nmodel of learning by converting the synaptic weight between $x$ and\n$x+\\hat{\\mu}$ to a dynamical Z(2) gauge variable $J_{x\\mu}$. The local Z(2)\ngauge symmetry is inherited from the Hopfield model and assures us the locality\nof time evolutions of $S_x$ and $J_{x\\mu}$ and a generalized Hebbian learning\nrule. At finite \"temperatures\", numerical simulations show that the model\nexhibits the Higgs, confinement, and Coulomb phases. We simulate dynamical\nprocesses of learning a pattern of $S_x$ and recalling it, and classify the\nparameter space according to the performance. At some parameter regions, stable\ncolumn-layer structures in signal propagations are spontaneously generated.\nMutual interactions between $S_x$ and $J_{x\\mu}$ induce partial memory loss as\nexpected.", "category": "cond-mat_dis-nn" }, { "text": "Super-Rough Glassy Phase of the Random Field XY Model in Two Dimensions: We study both analytically, using the renormalization group (RG) to two loop\norder, and numerically, using an exact polynomial algorithm, the\ndisorder-induced glass phase of the two-dimensional XY model with quenched\nrandom symmetry-breaking fields and without vortices. In the super-rough glassy\nphase, i.e. below the critical temperature $T_c$, the disorder and thermally\naveraged correlation function $B(r)$ of the phase field $\\theta(x)$, $B(r) =\n\\bar{<[\\theta(x) - \\theta(x+ r) ]^2>}$ behaves, for $r \\gg a$, as $B(r) \\simeq\nA(\\tau) \\ln^2 (r/a)$ where $r = |r|$ and $a$ is a microscopic length scale. We\nderive the RG equations up to cubic order in $\\tau = (T_c-T)/T_c$ and predict\nthe universal amplitude ${A}(\\tau) = 2\\tau^2-2\\tau^3 + {\\cal O}(\\tau^4)$. The\nuniversality of $A(\\tau)$ results from nontrivial cancellations between\nnonuniversal constants of RG equations. Using an exact polynomial algorithm on\nan equivalent dimer version of the model we compute ${A}(\\tau)$ numerically and\nobtain a remarkable agreement with our analytical prediction, up to $\\tau\n\\approx 0.5$.", "category": "cond-mat_dis-nn" }, { "text": "Low Temperature Properties of the Random Field Potts Chain: The random field q-States Potts model is investigated using exact\ngroundstates and finite-temperature transfer matrix calculations. It is found\nthat the domain structure and the Zeeman energy of the domains resembles for\ngeneral q the random field Ising case (q=2), which is also the expectation\nbased on a random-walk picture of the groundstate. The domain size distribution\nis exponential, and the scaling of the average domain size with the disorder\nstrength is similar for q arbitrary. The zero-temperature properties are\ncompared to the equilibrium spin states at small temperatures, to investigate\nthe effect of local random field fluctuations that imply locally degenerate\nregions. The response to field pertubabtions ('chaos') and the susceptibility\nare investigated. In particular for the chaos exponent it is found to be 1 for\nq = 2,...,5. Finally for q=2 (Ising case) the domain length distribution is\nstudied for correlated random fields.", "category": "cond-mat_dis-nn" }, { "text": "Deformation of inherent structures to detect long-range correlations in\n supercooled liquids: We propose deformations of inherent structures as a suitable tool for\ndetecting structural changes underlying the onset of cooperativity in\nsupercooled liquids. The non-affine displacement (NAD) field resulting from the\napplied deformation shows characteristic differences between the high\ntemperature liquid and supercooled state, that are typically observed in\ndynamic quantities. The average magnitude of the NAD is very sensitive to\ntemperature changes in the supercooled regime and is found to be strongly\ncorrelated with the inherent structure energy. In addition, the NAD field is\ncharacterized by a correlation length that increases upon lowering the\ntemperature towards the supercooled regime.", "category": "cond-mat_dis-nn" }, { "text": "Holes in a Quantum Spin Liquid: Magnetic neutron scattering provides evidence for nucleation of\nantiferromagnetic droplets around impurities in a doped nickel-oxide based\nquantum magnet. The undoped parent compound contains a spin liquid with a\ncooperative singlet ground state and a gap in the magnetic excitation spectrum.\nCalcium doping creates excitations below the gap with an incommensurate\nstructure factor. We show that weakly interacting antiferromagnetic droplets\nwith a central phase shift of $\\pi$ and a size controlled by the correlation\nlength of the quantum liquid can account for the data. The experiment provides\na first quantitative impression of the magnetic polarization cloud associated\nwith holes in a doped transition metal oxide.", "category": "cond-mat_dis-nn" }, { "text": "Soft annealing: A new approach to difficult computational problems: I propose a new method to study computationally difficult problems. I\nconsider a new system, larger than the one I want to simulate. The original\nsystem is recovered by imposing constraints on the large system. I simulate the\nlarge system with the hard constraints replaced by soft constraints. I\nillustrate the method in the case of the ferromagnetic Ising model and in the\ncase the three dimensional spin-glass model. I show that in both models the\nphases of the soft problem have the same properties as the phases of the\noriginal model and that the softened model belongs to the same universality\nclass as the original one. I show that correlation times are much shorter in\nthe larger soft constrained system and that it is computationally advantageous\nto study it instead of the original system. This method is quite general and\ncan be applied to many other systems.", "category": "cond-mat_dis-nn" }, { "text": "Dynamical Gauge Theory for the XY Gauge Glass Model: Dynamical systems of the gauge glass are investigated by the method of the\ngauge transformation.Both stochastic and deterministic dynamics are treated.\nSeveral exact relations are derived among dynamical quantities such as\nequilibrium and nonequilibrium auto-correlation functions, relaxation functions\nof order parameter and internal energy. They provide physical properties in\nterms of dynamics in the SG phase, a possible mixed phase and the Griffiths\nphase, the multicritical dynamics and the aging phenomenon. We also have a\nplausible argument for the absence of re-entrant transition in two or higher\ndimensions.", "category": "cond-mat_dis-nn" }, { "text": "On the number of limit cycles in asymmetric neural networks: The comprehension of the mechanisms at the basis of the functioning of\ncomplexly interconnected networks represents one of the main goals of\nneuroscience. In this work, we investigate how the structure of recurrent\nconnectivity influences the ability of a network to have storable patterns and\nin particular limit cycles, by modeling a recurrent neural network with\nMcCulloch-Pitts neurons as a content-addressable memory system.\n A key role in such models is played by the connectivity matrix, which, for\nneural networks, corresponds to a schematic representation of the \"connectome\":\nthe set of chemical synapses and electrical junctions among neurons. The shape\nof the recurrent connectivity matrix plays a crucial role in the process of\nstoring memories. This relation has already been exposed by the work of Tanaka\nand Edwards, which presents a theoretical approach to evaluate the mean number\nof fixed points in a fully connected model at thermodynamic limit.\nInterestingly, further studies on the same kind of model but with a finite\nnumber of nodes have shown how the symmetry parameter influences the types of\nattractors featured in the system. Our study extends the work of Tanaka and\nEdwards by providing a theoretical evaluation of the mean number of attractors\nof any given length $L$ for different degrees of symmetry in the connectivity\nmatrices.", "category": "cond-mat_dis-nn" }, { "text": "Vogel-Fulcher freezing in relaxor ferroelectrics: A physical mechanism for the freezing of polar nanoregions (PNRs) in relaxor\nferroelectrics is presented. Assuming that the activation energy for the\nreorientation of a cluster of PNRs scales with the mean volume of the cluster,\nthe characteristic relaxation time $\\tau$ is found to diverge as the cluster\nvolume reaches the percolation limit. Applying the mean field theory of\ncontinuum percolation, the familiar Vogel-Fulcher equation for the temperature\ndependence of $\\tau$ is derived.", "category": "cond-mat_dis-nn" }, { "text": "Complex topological features of reservoirs shape learning performances\n in bio-inspired recurrent neural networks: Recurrent networks are a special class of artificial neural systems that use\ntheir internal states to perform computing tasks for machine learning. One of\nits state-of-the-art developments, i.e. reservoir computing (RC), uses the\ninternal structure -- usually a static network with random structure -- to map\nan input signal into a nonlinear dynamical system defined in a higher\ndimensional space. Reservoirs are characterized by nonlinear interactions among\ntheir units and their ability to store information through recurrent loops,\nallowing to train artificial systems to learn task-specific dynamics. However,\nit is fundamentally unknown how the random topology of the reservoir affects\nthe learning performance. Here, we fill this gap by considering a battery of\nsynthetic networks -- characterized by different topological features -- and 45\nempirical connectomes -- sampled from brain regions of organisms belonging to 8\ndifferent species -- to build the reservoir and testing the learning\nperformance against a prediction task with a variety of complex input signals.\nWe find nontrivial correlations between RC performances and both the number of\nnodes and rank of the covariance matrix of activation states, with performance\ndepending on the nature -- stochastic or deterministic -- of input signals.\nRemarkably, the modularity and the link density of the reservoir are found to\naffect RC performances: these results cannot be predicted by models only\naccounting for simple topological features of the reservoir. Overall, our\nfindings highlight that the complex topological features characterizing\nbiophysical computing systems such as connectomes can be used to design\nefficient bio-inspired artificial neural networks.", "category": "cond-mat_dis-nn" }, { "text": "Universal Transport Dynamics of Complex Fluids: Thermal motion in complex fluids is a complicated stochastic process but\nubiquitously exhibits initial ballistic, intermediate sub-diffusive, and\nlong-time non-Gaussian diffusive motion, unless interrupted. Despite its\nrelevance to numerous dynamical processes of interest in modern science, a\nunified, quantitative understanding of thermal motion in complex fluids remains\na long-standing problem. Here, we present a new transport equation and its\nsolutions, which yield a unified quantitative explanation of the mean square\ndisplacement (MSD) and the non-Gaussian parameter (NGP) of various fluid\nsystems. We find the environment-coupled diffusion kernel and its time\ncorrelation function are two essential quantities determining transport\ndynamics of complex fluids. From our analysis, we construct a general, explicit\nmodel of the complex fluid transport dynamics. This model quantitatively\nexplains not only the MSD and NGP, but also the time-dependent relaxation of\nthe displacement distribution for various systems. We introduce the concepts of\nintrinsic disorder and extrinsic disorder that have distinct effects on\ntransport dynamics and different dependencies on temperature and density. This\nwork presents a new paradigm for quantitative understanding of transport and\ntransport-coupled processes in complex disordered media.", "category": "cond-mat_dis-nn" }, { "text": "Unlearning regularization for Boltzmann Machines: Boltzmann Machines (BMs) are graphical models with interconnected binary\nunits, employed for the unsupervised modeling of data distributions. When\ntrained on real data, BMs show the tendency to behave like critical systems,\ndisplaying a high susceptibility of the model under a small rescaling of the\ninferred parameters. This behaviour is not convenient for the purpose of\ngenerating data, because it slows down the sampling process, and induces the\nmodel to overfit the training-data. In this study, we introduce a\nregularization method for BMs to improve the robustness of the model under\nrescaling of the parameters. The new technique shares formal similarities with\nthe unlearning algorithm, an iterative procedure used to improve memory\nassociativity in Hopfield-like neural networks. We test our unlearning\nregularization on synthetic data generated by two simple models, the\nCurie-Weiss ferromagnetic model and the Sherrington-Kirkpatrick spin glass\nmodel, and we show that it outperforms $L_p$-norm schemes. Finally, we discuss\nthe role of parameter initialization.", "category": "cond-mat_dis-nn" }, { "text": "Simplified dynamics for glass model: In spin glass models one can remove minimization of free energy by some order\nparameter. One can consider hierarchy of order parameters. It is possible to\ndivide energy among these parts. We can consider relaxation process in glass\nsystem phenomonologically, as exchange of energy between 2 parts. It is\npossible to identify trap points in phase space. We suggest some\nphenomonological approximation-truncated Langevine.\n The mean field statics is used to introduce a phenomenologic dynamics as its\nnatural extension.\n Purely kinetical phase transitions are investigated..", "category": "cond-mat_dis-nn" }, { "text": "Anchored advected interfaces, Oslo model, and roughness at depinning: There is a plethora of 1-dimensional advected systems with an absorbing\nboundary: the Toom model of anchored interfaces, the directed exclusion process\nwhere in addition to diffusion particles and holes can jump over their right\nneighbor, simple diffusion with advection, and Oslo sandpiles. All these models\nshare a roughness exponent of $\\zeta=1/4$, while the dynamic exponent $z$\nvaries, depending on the observable. We show that for the first three models\n$z=1$, $z=2$, and $z=1/2$ are realized, depending on the observable. The Oslo\nmodel is apart with a conjectured dynamic exponent of $z=10/7$. Since the\nheight in the latter is the gradient of the position of a disordered elastic\nstring, this shows that $\\zeta =5/4$ for a driven elastic string at depinning.", "category": "cond-mat_dis-nn" }, { "text": "Effect of Nuclear Quadrupole Interaction on the Relaxation in Amorphous\n Solids: Recently it has been experimentally demonstrated that certain glasses display\nan unexpected magnetic field dependence of the dielectric constant. In\nparticular, the echo technique experiments have shown that the echo amplitude\ndepends on the magnetic field. The analysis of these experiments results in the\nconclusion that the effect seems to be related to the nuclear degrees of\nfreedom of tunneling systems. The interactions of a nuclear quadrupole\nelectrical moment with the crystal field and of a nuclear magnetic moment with\nmagnetic field transform the two-level tunneling systems inherent in amorphous\ndielectrics into many-level tunneling systems. The fact that these features\nshow up at temperatures $T<100mK$, where the properties of amorphous materials\nare governed by the long-range $R^{-3}$ interaction between tunneling systems,\nsuggests that this interaction is responsible for the magnetic field dependent\nrelaxation. We have developed a theory of many-body relaxation in an ensemble\nof interacting many-level tunneling systems and show that the relaxation rate\nis controlled by the magnetic field. The results obtained correlate with the\navailable experimental data. Our approach strongly supports the idea that the\nnuclear quadrupole interaction is just the key for understanding the unusual\nbehavior of glasses in a magnetic field.", "category": "cond-mat_dis-nn" }, { "text": "Understanding spin glass transition as a dynamic phenomenon: Existing theories explain spin glass transition in terms of a phase\ntransition and order parameters, and assume the existence of a distinct spin\nglass phase. In addition to problems related to clarifying the nature of this\nphase, the common challenge is to explain profound dynamic effects. Here, we\npropose that the main experimental results of spin glass transition can be\nunderstood in an entirely dynamic picture, without a reference to a distinct\nspin glass phase, phase transition and order parameters. In this theory, the\nsusceptibility cusp at the glass transition temperature is due to the dynamic\ncrossover between the high-temperature relaxational and low-temperature spin\nwave, or elastic, regime. The crossover takes place when $t=\\tau$, where $t$ is\nobservation time and $\\tau$ is relaxation time. Time-dependent effects,\ninconsistent with the phase transition approach, and the logarithmic increase\nof $T_g$ with field frequency in particular, originate as the immediate\nconsequence of the proposed picture. We comment on the behavior of non-linear\nsusceptibility. In our discussion, we explore similarities between the spin and\nstructural glass transitions.", "category": "cond-mat_dis-nn" }, { "text": "Effective transport properties of conformal Voronoi-bounded columns via\n recurrent boundary element expansions: Effective transport properties of heterogeneous structures are predicted by\ngeometric microstructural parameters, but these can be difficult to calculate.\nHere, a boundary element code with a recurrent series method accurately and\nefficiently determines the high order parameters of polygonal and conformal\nprisms in regular two-dimensional lattices and Voronoi tessellations (VT). This\nreveals that proximity to simpler estimates is associated with: centroidal VT\n(cf random VT), compactness, and VT structures (cf similarly compact\nsemi-regular lattices). An error in previously reported values for triangular\nlattices is noted.", "category": "cond-mat_dis-nn" }, { "text": "Electrodynamics of a Coulomb Glass in n-type Silicon: Optical measurements of the real and imaginary frequency dependent\nconductivity of uncompensated n-type silicon are reported. The experiments are\ndone in the quantum limit, $ \\hbar\\omega > k_{B}T$, across a broad doping range\non the insulating side of the Metal-Insulator transition (MIT). The observed\nlow energy linear frequency dependence shows characteristics consistent with\ntheories of a Coulomb glass, but discrepancies exist in the relative magnitudes\nof the real and imaginary components. At higher energies we observe a crossover\nto a quadratic frequency dependence that is sharper than expected over the\nentire dopant range. The concentration dependence gives evidence that the\nCoulomb interaction energy is the relevant energy scale that determines this\ncrossover.", "category": "cond-mat_dis-nn" }, { "text": "Electromagnetic Waves Through Disordered Systems: Comparison Of\n Intensity, Transmission And Conductance: We obtain the statistics of the intensity, transmission and conductance for\nscalar electromagnetic waves propagating through a disordered collection of\nscatterers. Our results show that the probability distribution for these\nquantities, x, follow a universal form x^a Exp(-x^m) . This family of functions\nincludes the Rayleigh distribution (when a=0, m=1) and the Dirac delta function\n(a -> Infinity), which are the expressions for intensity and transmission in\nthe diffusive regime neglecting correlations. Finally, we find simple\nanalytical expressions for the nth moment of the distributions and for to the\nratio of the moments of the intensity and transmission, which generalizes the\nn! result valid in the above regime.", "category": "cond-mat_dis-nn" }, { "text": "Correlated Persistent Tunneling Currents in Glasses: Low temperature properties of glasses are derived within a generalized\ntunneling model, considering the motion of charged particles on a closed path\nin a double-well potential. The presence of a magnetic induction field B\nviolates the time reversal invariance due to the Aharonov-Bohm phase, and leads\nto flux periodic energy levels. At low temperature, this effect is shown to be\nstrongly enhanced by dipole-dipole and elastic interactions between tunneling\nsystems and becomes measurable. Thus, the recently observed strong sensitivity\nof the electric permittivity to weak magnetic fields can be explained. In\naddition, superimposed oscillations as a function of the magnetic field are\npredicted.", "category": "cond-mat_dis-nn" }, { "text": "Continuum Percolation on Disoriented Surfaces: the Problem of Permeable\n Disks on a Klein Bottle: The percolation threshold and wrapping probability $R_{\\infty}$ for the\ntwo-dimensional problem of continuum percolation on the surface of a Klein\nbottle have been calculated by the Monte Carlo method with the Newman--Ziff\nalgorithm for completely permeable disks. It has been shown that the\npercolation threshold of disks on the Klein bottle coincides with the\npercolation threshold of disks on the surface of a torus, indicating that this\nthreshold is topologically invariant. The scaling exponents determining\ncorrections to the wrapping probability and critical concentration owing to the\nfinite-size effects are also topologically invariant. At the same time, the\nquantities $R_{\\infty}$ are different for percolation on the torus and Klein\nbottle and are apparently determined by the topology of the surface.\nFurthermore, the difference between the $R_{\\infty}$ values for the torus and\nKlein bottle means that at least one of the percolation clusters is degenerate.", "category": "cond-mat_dis-nn" }, { "text": "Phase boundary near a magnetic percolation transition: Motivated by recent experimental observations [Phys. Rev. 96, 020407 (2017)]\non hexagonal ferrites, we revisit the phase diagrams of diluted magnets close\nto the lattice percolation threshold. We perform large-scale Monte Carlo\nsimulations of XY and Heisenberg models on both simple cubic lattices and\nlattices representing the crystal structure of the hexagonal ferrites. Close to\nthe percolation threshold $p_c$, we find that the magnetic ordering temperature\n$T_c$ depends on the dilution $p$ via the power law $T_c \\sim |p-p_c|^\\phi$\nwith exponent $\\phi=1.09$, in agreement with classical percolation theory.\nHowever, this asymptotic critical region is very narrow, $|p-p_c| \\lesssim\n0.04$. Outside of it, the shape of the phase boundary is well described, over a\nwide range of dilutions, by a nonuniversal power law with an exponent somewhat\nbelow unity. Nonetheless, the percolation scenario does not reproduce the\nexperimentally observed relation $T_c \\sim (x_c -x)^{2/3}$ in\nPbFe$_{12-x}$Ga$_x$O$_{19}$. We discuss the generality of our findings as well\nas implications for the physics of diluted hexagonal ferrites.", "category": "cond-mat_dis-nn" }, { "text": "Design of one-dimensional Lambertian diffusers of light: We describe a method for designing a one-dimensional random surface that acts\nas a Lambertian diffuser. The method is tested by means of rigorous computer\nsimulations and is shown to yield the desired scattering pattern.", "category": "cond-mat_dis-nn" }, { "text": "Evidence for growth of collective excitations in glasses at low\n temperatures: We present new data on the nonequilibrium acoustic response of glasses to an\napplied dc electric field below 1K. When compared with the analogous dielectric\nresponse of the same material, the acoustic data show, within experimental\nprecision, identical dependence on the perturbing field, but stronger\ntemperature dependence. These data are difficult to reconcile with simple\ngeneralizations of the dipole gap model of two-level system (TLS) dielectric\nresponse, unless we assume that as T is decreased, interaction-based TLS\ncollective effects increase.", "category": "cond-mat_dis-nn" }, { "text": "Quantum fluctuations in the transverse Ising spin glass model: A field\n theory of random quantum spin systems: We develop a mean-field theory for random quantum spin systems using the spin\ncoherent state path integral representation. After the model is reduced to the\nmean field one-body Hamiltonian, the integral is analyzed with the aid of\nseveral methods such as the semiclassical method and the gauge transformation.\nAs an application we consider the Sherrington-Kirkpatrick model in a transverse\nfield. Using the Landau expansion and its improved versions, we give a detailed\nanalysis of the imaginary-time dependence of the order parameters. Integrating\nout the quantum part of the order parameters, we obtain the effective\nrenormalized free energy written in terms of the classically defined order\nparameters. Our method allows us to obtain the spin glass-paramagnetic phase\ntransition point $\\Gamma/J\\sim 1.62$ at T=0.", "category": "cond-mat_dis-nn" }, { "text": "On the origin of the $\u03bb$-transition in liquid Sulphur: Developing a novel experimental technique, we applied photon correlation\nspectroscopy using infrared radiation in liquid Sulphur around $T_\\lambda$,\ni.e. in the temperature range where an abrupt increase in viscosity by four\norders of magnitude is observed upon heating within few degrees. This allowed\nus - overcoming photo-induced and absorption effects at visible wavelengths -\nto reveal a chain relaxation process with characteristic time in the ms range.\nThese results do rehabilitate the validity of the Maxwell relation in Sulphur\nfrom an apparent failure, allowing rationalizing the mechanical and\nthermodynamic behavior of this system within a viscoelastic scenario.", "category": "cond-mat_dis-nn" }, { "text": "Magnetoresistance in semiconductor structures with hopping conductivity:\n effects of random potential and generalization for the case of acceptor\n states: We reconsider the theory of magnetoresistance in hopping semiconductors.\nFirst, we have shown that the random potential of the background impurities\naffects significantly preexponential factor of the tunneling amplitude which\nbecomes to be a short-range one in contrast to the long-range one for purely\nCoulomb hopping centers. This factor to some extent suppresses the negative\ninterference magnetoresistance and can lead to its decrease with temperature\ndecrease which is in agreement with earlier experimental observations. We have\nalso extended the theoretical models of positive spin magnetoresistance, in\nparticular, related to a presence of doubly occupied states (corresponding to\nthe upper Hubbard band) to the case of acceptor states in 2D structures. We\nhave shown that this mechanism can dominate over classical wave-shrinkage\nmagnetoresistance at low temperatures. Our results are in semi-quantitative\nagreement with experimental data.", "category": "cond-mat_dis-nn" }, { "text": "Quantitative field theory of the glass transition: We develop a full microscopic replica field theory of the dynamical\ntransition in glasses. By studying the soft modes that appear at the dynamical\ntemperature we obtain an effective theory for the critical fluctuations. This\nanalysis leads to several results: we give expressions for the mean field\ncritical exponents, and we study analytically the critical behavior of a set of\nfour-points correlation functions from which we can extract the dynamical\ncorrelation length. Finally, we can obtain a Ginzburg criterion that states the\nrange of validity of our analysis. We compute all these quantities within the\nHypernetted Chain Approximation (HNC) for the Gibbs free energy and we find\nresults that are consistent with numerical simulations.", "category": "cond-mat_dis-nn" }, { "text": "A numerical study of the overlap probability distribution and its\n sample-to-sample fluctuations in a mean-field model: In this paper we study the fluctuations of the probability distributions of\nthe overlap in mean field spin glasses in the presence of a magnetic field on\nthe De Almeida-Thouless line. We find that there is a large tail in the left\npart of the distribution that is dominated by the contributions of rare\nsamples. Different techniques are used to examine the data and to stress on\ndifferent aspects of the contribution of rare samples.", "category": "cond-mat_dis-nn" }, { "text": "Spatial correlation functions and dynamical exponents in very large\n samples of 4D spin glasses: The study of the low temperature phase of spin glass models by means of Monte\nCarlo simulations is a challenging task, because of the very slow dynamics and\nthe severe finite size effects they show. By exploiting at the best the\ncapabilities of standard modern CPUs (especially the SSE instructions), we have\nbeen able to simulate the four-dimensional (4D) Edwards-Anderson model with\nGaussian couplings up to sizes $L=70$ and for times long enough to accurately\nmeasure the asymptotic behavior. By quenching systems of different sizes to the\nthe critical temperature and to temperatures in the whole low temperature\nphase, we have been able to identify the regime where finite size effects are\nnegligible: $\\xi(t) \\lesssim L/7$. Our estimates for the dynamical exponent ($z\n\\simeq 1/T$) and for the replicon exponent ($\\alpha \\simeq 1.0$ and\n$T$-independent), that controls the decay of the spatial correlation in the\nzero-overlap sector, are consistent with the RSB theory, but the latter differs\nfrom the theoretically conjectured value.", "category": "cond-mat_dis-nn" }, { "text": "Continuum Percolation on Disoriented Surfaces: the Problem of Permeable\n Disks on a Klein Bottle: The percolation threshold and wrapping probability $R_{\\infty}$ for the\ntwo-dimensional problem of continuum percolation on the surface of a Klein\nbottle have been calculated by the Monte Carlo method with the Newman--Ziff\nalgorithm for completely permeable disks. It has been shown that the\npercolation threshold of disks on the Klein bottle coincides with the\npercolation threshold of disks on the surface of a torus, indicating that this\nthreshold is topologically invariant. The scaling exponents determining\ncorrections to the wrapping probability and critical concentration owing to the\nfinite-size effects are also topologically invariant. At the same time, the\nquantities $R_{\\infty}$ are different for percolation on the torus and Klein\nbottle and are apparently determined by the topology of the surface.\nFurthermore, the difference between the $R_{\\infty}$ values for the torus and\nKlein bottle means that at least one of the percolation clusters is degenerate.", "category": "cond-mat_dis-nn" }, { "text": "Localization crossover and subdiffusive transport in a classical\n facilitated network model of a disordered, interacting quantum spin chain: We consider the random-field Heisenberg model, a paradigmatic model for\nmany-body localization (MBL), and add a Markovian dephasing bath coupled to the\nAnderson orbitals of the model's non-interacting limit. We map this system to a\nclassical facilitated hopping model that is computationally tractable for large\nsystem sizes, and investigate its dynamics. The classical model exhibits a\nrobust crossover between an ergodic (thermal) phase and a frozen (localized)\nphase. The frozen phase is destabilized by thermal subregions (bubbles), which\nthermalize surrounding sites by providing a fluctuating interaction energy and\nso enable off-resonance particle transport. Investigating steady state\ntransport, we observe that the interplay between thermal and frozen bubbles\nleads to a clear transition between diffusive and subdiffusive regimes. This\nphenomenology both describes the MBL system coupled to a bath, and provides a\nclassical analogue for the many-body localization transition in the\ncorresponding quantum model, in that the classical model displays long local\nmemory times. It also highlights the importance of the details of the bath\ncoupling in studies of MBL systems coupled to thermal environments.", "category": "cond-mat_dis-nn" }, { "text": "Annealed inhomogeneities in random ferromagnets: We consider spin models on complex networks frequently used to model social\nand technological systems. We study the annealed ferromagnetic Ising model for\nrandom networks with either independent edges (Erd\\H{o}s-R\\'enyi), or with\nprescribed degree distributions (configuration model). Contrary to many\nphysical models, the annealed setting is poorly understood and behaves quite\ndifferently than the quenched system. In annealed networks with a fluctuating\nnumber of edges, the Ising model changes the degree distribution, an aspect\npreviously ignored. For random networks with Poissonian degrees, this gives\nrise to three distinct annealed critical temperatures depending on the precise\nmodel choice, only one of which reproduces the quenched one. In particular, two\nof these annealed critical temperatures are finite even when the quenched one\nis infinite, since then the annealed graph creates a giant component for all\nsufficiently small temperatures. We see that the critical exponents in the\nconfiguration model with deterministic degrees are the same as the quenched\nones, which are the mean-field exponents if the degree distribution has finite\nfourth moment, and power-law-dependent critical exponents otherwise.\nRemarkably, the annealing for the configuration model with random i.i.d.\ndegrees washes away the universality class with power-law critical exponents.", "category": "cond-mat_dis-nn" }, { "text": "Metal-Insulator-Transition in a Weakly interacting Disordered Electron\n System: The interplay of interactions and disorder is studied using the\nAnderson-Hubbard model within the typical medium dynamical cluster\napproximation. Treating the interacting, non-local cluster self-energy\n($\\Sigma_c[{\\cal \\tilde{G}}](i,j\\neq i)$) up to second order in the\nperturbation expansion of interactions, $U^2$, with a systematic incorporation\nof non-local spatial correlations and diagonal disorder, we explore the initial\neffects of electron interactions ($U$) in three dimensions. We find that the\ncritical disorder strength ($W_c^U$), required to localize all states,\nincreases with increasing $U$; implying that the metallic phase is stabilized\nby interactions. Using our results, we predict a soft pseudogap at the\nintermediate $W$ close to $W_c^U$ and demonstrate that the mobility edge\n($\\omega_\\epsilon$) is preserved as long as the chemical potential, $\\mu$, is\nat or beyond the mobility edge energy.", "category": "cond-mat_dis-nn" }, { "text": "Enhancement of the Magnetocaloric Effect in Geometrically Frustrated\n Cluster Spin Glass Systems: In this work, we theoretically demonstrate that a strong enhancement of the\nMagnetocaloric Effect is achieved in geometrically frustrated cluster\nspin-glass systems just above the freezing temperature. We consider a network\nof clusters interacting randomly which have triangular structure composed of\nIsing spins interacting antiferromagnetically. The intercluster disorder\nproblem is treated using a cluster spin glass mean-field theory, which allows\nexact solution of the disordered problem. The intracluster part can be solved\nusing exact enumeration. The coupling between the inter and intracluster\nproblem incorporates the interplay between effects coming from geometric\nfrustration and disorder. As a result, it is shown that there is the onset of\ncluster spin glass phase even with very weak disorder. Remarkably, it is\nexactly within a range of very weak disorder and small magnetic field that is\nobserved the strongest isothermal release of entropy.", "category": "cond-mat_dis-nn" }, { "text": "Calculation of ground states of four-dimensional +or- J Ising spin\n glasses: Ground states of four-dimensional (d=4) EA Ising spin glasses are calculated\nfor sizes up to 7x7x7x7 using a combination of a genetic algorithm and\ncluster-exact approximation. The ground-state energy of the infinite system is\nextrapolated as e_0=-2.095(1). The ground-state stiffness (or domain wall)\nenergy D is calculated. A D~L^{\\Theta} behavior with \\Theta=0.65(4) is found\nwhich confirms that the d=4 model has an equilibrium spin-glass-paramagnet\ntransition for non-zero T_c.", "category": "cond-mat_dis-nn" }, { "text": "Adaptive Density-Matrix Renormalization-Group study of the disordered\n antiferromagnetic spin-1/2 Heisenberg chain: Using the recently introduced adaptive density-matrix renormalization-group\nmethod, we study the many spin-spin correlations of the spin-$1/2$\nantiferromagnetic Heisenberg chain with random coupling constants, namely, the\nmean value of the bulk and of the end-to-end correlations, the typical value of\nthe bulk correlations, and the distribution of the bulk correlations. Our\nresults are in striking agreement with the predictions of the strong-disorder\nrenormalization group method. We do not find any hint of logarithmic\ncorrections neither in the bulk average correlations, which were recently\nreported by Shu et al. [Phys. Rev. B 94,174442 (2016)], nor in the end-to-end\naverage correlations. We report computed the existence of logarithmic\ncorrection on the end-to-end correlations of the clean chain. Finally, we have\ndetermined that the distribution of the bulk correlations, when properly\nrescaled by an associated Lyapunov exponent, is a narrow and universal\n(disorder-independent) probability function.", "category": "cond-mat_dis-nn" }, { "text": "Effect of selection on ancestry: an exactly soluble case and its\n phenomenological generalization: We consider a family of models describing the evolution under selection of a\npopulation whose dynamics can be related to the propagation of noisy traveling\nwaves. For one particular model, that we shall call the exponential model, the\nproperties of the traveling wave front can be calculated exactly, as well as\nthe statistics of the genealogy of the population. One striking result is that,\nfor this particular model, the genealogical trees have the same statistics as\nthe trees of replicas in the Parisi mean-field theory of spin glasses. We also\nfind that in the exponential model, the coalescence times along these trees\ngrow like the logarithm of the population size. A phenomenological picture of\nthe propagation of wave fronts that we introduced in a previous work, as well\nas our numerical data, suggest that these statistics remain valid for a larger\nclass of models, while the coalescence times grow like the cube of the\nlogarithm of the population size.", "category": "cond-mat_dis-nn" }, { "text": "Efficient Representation of Quantum Many-body States with Deep Neural\n Networks: The challenge of quantum many-body problems comes from the difficulty to\nrepresent large-scale quantum states, which in general requires an\nexponentially large number of parameters. Recently, a connection has been made\nbetween quantum many-body states and the neural network representation\n(\\textit{arXiv:1606.02318}). An important open question is what characterizes\nthe representational power of deep and shallow neural networks, which is of\nfundamental interest due to popularity of the deep learning methods. Here, we\ngive a rigorous proof that a deep neural network can efficiently represent most\nphysical states, including those generated by any polynomial size quantum\ncircuits or ground states of many body Hamiltonians with polynomial-size gaps,\nwhile a shallow network through a restricted Boltzmann machine cannot\nefficiently represent those states unless the polynomial hierarchy in\ncomputational complexity theory collapses.", "category": "cond-mat_dis-nn" }, { "text": "Topological phases and Anderson localization in off-diagonal mosaic\n lattices: We introduce a one-dimensional lattice model whose hopping amplitudes are\nmodulated for equally spaced sites. Such mosaic lattice exhibits many\ninteresting topological and localization phenomena that do not exist in the\nregular off-diagonal lattices. When the mosaic modulation is commensurate with\nthe underlying lattice, topologically nontrivial phases with zero- and\nnonzero-energy edge modes are observed as we tune the modulation, where the\nnontrivial regimes are characterized by quantized Berry phases. If the mosaic\nlattice becomes incommensurate, Anderson localization will be induced purely by\nthe quasiperiodic off-diagonal modulations. The localized eigenstate is found\nto be centered on two neighboring sites connected by the quasiperiodic hopping\nterms. Furthermore, both the commensurate and incommensurate off-diagonal\nmosaic lattices can host Chern insulators in their two-dimensional\ngeneralizations. Our work provides a platform for exploring topological phases\nand Anderson localization in low-dimensional systems.", "category": "cond-mat_dis-nn" }, { "text": "Enhancement of chaotic subdiffusion in disordered ladders with synthetic\n gauge fields: We study spreading wave packets in a disordered nonlinear ladder with broken\ntime-reversal symmetry induced by synthetic gauge fields. The model describes\nthe dynamics of interacting bosons in a disordered and driven optical ladder\nwithin a mean-field approximation. The second moment of the wave packet $m_{2}\n= g t^{\\alpha}$ grows subdiffusively with the universal exponent $\\alpha \\simeq\n1/3$ similar to the time-reversal case. However the prefactor $g$ is strongly\nmodified by the field strength and shows a non-monotonic dependence. For a weak\nfield, the prefactor increases since time-reversal enhanced backscattering is\nsuppressed. For strong fields the spectrum of the linear wave equation reduces\nthe localization length through the formation of gaps and narrow bands.\nConsequently the prefactor for the subdiffusive spreading law is suppressed.", "category": "cond-mat_dis-nn" }, { "text": "Avalanches and many-body resonances in many-body localized systems: We numerically study both the avalanche instability and many-body resonances\nin strongly-disordered spin chains exhibiting many-body localization (MBL). We\ndistinguish between a finite-size/time MBL regime, and the asymptotic MBL\nphase, and identify some \"landmarks\" within the MBL regime. Our first landmark\nis an estimate of where the MBL phase becomes unstable to avalanches, obtained\nby measuring the slowest relaxation rate of a finite chain coupled to an\ninfinite bath at one end. Our estimates indicate that the actual MBL-to-thermal\nphase transition, in infinite-length systems, occurs much deeper in the MBL\nregime than has been suggested by most previous studies. Our other landmarks\ninvolve system-wide resonances. We find that the effective matrix elements\nproducing eigenstates with system-wide resonances are enormously broadly\ndistributed. This means that the onset of such resonances in typical samples\noccurs quite deep in the MBL regime, and the first such resonances typically\ninvolve rare pairs of eigenstates that are farther apart in energy than the\nminimum gap. Thus we find that the resonance properties define two landmarks\nthat divide the MBL regime in to three subregimes: (i) at strongest disorder,\ntypical samples do not have any eigenstates that are involved in system-wide\nmany-body resonances; (ii) there is a substantial intermediate regime where\ntypical samples do have such resonances, but the pair of eigenstates with the\nminimum spectral gap does not; and (iii) in the weaker randomness regime, the\nminimum gap is involved in a many-body resonance and thus subject to level\nrepulsion. Nevertheless, even in this third subregime, all but a vanishing\nfraction of eigenstates remain non-resonant and the system thus still appears\nMBL in many respects. Based on our estimates of the location of the avalanche\ninstability, it might be that the MBL phase is only part of subregime (i).", "category": "cond-mat_dis-nn" }, { "text": "A pragmatical access to the viscous flow: The paper derives a relation for the viscosity of undercooled liquids on the\nbasis of the pragmatical model concept of Eshelby relaxations with a finite\nlifetime. From accurate shear relaxation data in the literature, one finds that\nslightly less than half of the internal stresses relax directly via single\nEshelby relaxations; the larger part dissolves at the terminal lifetime, which\nis a combined effect of many Eshelby relaxations.", "category": "cond-mat_dis-nn" }, { "text": "Monte Carlo studies of the one-dimensional Ising spin glass with\n power-law interactions: We present results from Monte Carlo simulations of the one-dimensional Ising\nspin glass with power-law interactions at low temperature, using the parallel\ntempering Monte Carlo method. For a set of parameters where the long-range part\nof the interaction is relevant, we find evidence for large-scale droplet-like\nexcitations with an energy that is independent of system size, consistent with\nreplica symmetry breaking. We also perform zero-temperature defect energy\ncalculations for a range of parameters and find a stiffness exponent for domain\nwalls in reasonable, but by no means perfect agreement with analytic\npredictions.", "category": "cond-mat_dis-nn" }, { "text": "Fixed points and their stability in the functional renormalization group\n of random field models: We consider the zero-temperature fixed points controlling the critical\nbehavior of the $d$-dimensional random-field Ising, and more generally $O(N)$,\nmodels. We clarify the nature of these fixed points and their stability in the\nregion of the $(N,d)$ plane where one passes from a critical behavior\nsatisfying the $d\\rightarrow d-2$ dimensional reduction to one where it breaks\ndown due to the appearance of strong enough nonanalyticities in the functional\ndependence of the cumulants of the renormalized disorder. We unveil an\nintricate and unusual behavior.", "category": "cond-mat_dis-nn" }, { "text": "Equilibrium valleys in spin glasses at low temperature: We investigate the 3-dimensional Edwards-Anderson spin glass model at low\ntemperature on simple cubic lattices of sizes up to L=12. Our findings show a\nstrong continuity among T>0 physical features and those found previously at\nT=0, leading to a scenario with emerging mean field like characteristics that\nare enhanced in the large volume limit. For instance, the picture of space\nfilling sponges seems to survive in the large volume limit at T>0, while\nentropic effects play a crucial role in determining the free-energy degeneracy\nof our finite volume states. All of our analysis is applied to equilibrium\nconfigurations obtained by a parallel tempering on 512 different disorder\nrealizations. First, we consider the spatial properties of the sites where\npairs of independent spin configurations differ and we introduce a modified\nspin overlap distribution which exhibits a non-trivial limit for large L.\nSecond, after removing the Z_2 (+-1) symmetry, we cluster spin configurations\ninto valleys. On average these valleys have free-energy differences of O(1),\nbut a difference in the (extensive) internal energy that grows significantly\nwith L; there is thus a large interplay between energy and entropy\nfluctuations. We also find that valleys typically differ by sponge-like space\nfilling clusters, just as found previously for low-energy system-size\nexcitations above the ground state.", "category": "cond-mat_dis-nn" }, { "text": "Density of States near the Anderson Transition in a Four-dimensional\n Space. Renormalizable Models: Asymptotically exact results are obtained for the average Green function and\ndensity of states of a disordered system for a renormalizable class of models\n(as opposed to the lattice models examined previously [Zh. Eksp. Teor. Fiz. 106\n(1994) 560-584]). For N\\sim 1 (where N is an order of the perturbation theory),\nonly the parquet terms corresponding to the highest powers of large logarithms\nare retained. For large N, this approximation is inadequate because of the fast\ngrowth with N of the coefficients for the lower powers of the logarithms. The\nlatter coefficients are calculated in the leading order in N from the\nCallan-Symanzik equation with results of the Lipatov method using as boundary\nconditions. For calculating the self-energy at finite momentum, a modification\nof the parquet approximation is used, that allows the calculations to be done\nin an arbitrary finite logarithmic approximation but in the leading order in N.\nIt is shown that the phase transition point shifts in the complex plane,\nthereby insuring regularity of the density of states for all energies. The\n\"spurious\" pole is avoided in such a way that effective interaction remains\nlogarithmically weak.", "category": "cond-mat_dis-nn" }, { "text": "Zero-Temperature Critical Phenomena in Two-Dimensional Spin Glasses: Recent developments in study of two-dimensional spin glass models are\nreviewed in light of fractal nature of droplets at zero-temperature. Also\npresented are some new results including a new estimate of the stiffness\nexponent using a boundary condition different from conventional ones.", "category": "cond-mat_dis-nn" }, { "text": "Quasi-long range order in the random anisotropy Heisenberg model: The large distance behaviors of the random field and random anisotropy\nHeisenberg models are studied with the functional renormalization group in\n$4-\\epsilon$ dimensions. The random anisotropy model is found to have a phase\nwith the infinite correlation radius at low temperatures and weak disorder. The\ncorrelation function of the magnetization obeys a power law $<{\\bf m}({\\bf\nr}_1) {\\bf m}({\\bf r}_2)>\\sim| {\\bf r}_1-{\\bf r}_2|^{-0.62\\epsilon}$. The\nmagnetic susceptibility diverges at low fields as $\\chi\\sim\nH^{-1+0.15\\epsilon}$. In the random field model the correlation radius is found\nto be finite at the arbitrarily weak disorder.", "category": "cond-mat_dis-nn" }, { "text": "Comment on \"Evidence of Non-Mean-Field-Like Low-Temperature Behavior in\n the Edwards-Anderson Spin-Glass Model\": A recent interesting paper [Yucesoy et al. Phys. Rev. Lett. 109, 177204\n(2012), arXiv:1206:0783] compares the low-temperature phase of the 3D\nEdwards-Anderson (EA) model to its mean-field counterpart, the\nSherrington-Kirkpatrick (SK) model. The authors study the overlap distributions\nP_J(q) and conclude that the two models behave differently. Here we notice that\na similar analysis using state-of-the-art, larger data sets for the EA model\n(generated with the Janus computer) leads to a very clear interpretation of the\nresults of Yucesoy et al., showing that the EA model behaves as predicted by\nthe replica symmetry breaking (RSB) theory.", "category": "cond-mat_dis-nn" }, { "text": "Solvable model of a polymer in random media with long ranged disorder\n correlations: We present an exactly solvable model of a Gaussian (flexible) polymer chain\nin a quenched random medium. This is the case when the random medium obeys very\nlong range quadratic correlations. The model is solved in $d$ spatial\ndimensions using the replica method, and practically all the physical\nproperties of the chain can be found. In particular the difference between the\nbehavior of a chain that is free to move and a chain with one end fixed is\nelucidated. The interesting finding is that a chain that is free to move in a\nquadratically correlated random potential behaves like a free chain with $R^2\n\\sim L$, where $R$ is the end to end distance and $L$ is the length of the\nchain, whereas for a chain anchored at one end $R^2 \\sim L^4$. The exact\nresults are found to agree with an alternative numerical solution in $d=1$\ndimensions. The crossover from long ranged to short ranged correlations of the\ndisorder is also explored.", "category": "cond-mat_dis-nn" }, { "text": "Metal-insulator transition in hydrogenated graphene as manifestation of\n quasiparticle spectrum rearrangement of anomalous type: We demonstrate that the spectrum rearrangement can be considered as a\nprecursor of the metal-insulator transition observed in graphene dosed with\nhydrogen atoms. The Anderson-type transition is attributed to the coincidence\nbetween the Fermi level and the mobility edge, which appearance is induced by\nthe spectrum rearrangement. Available experimental data are thoroughly compared\nto the theoretical results for the Lifshitz impurity model.", "category": "cond-mat_dis-nn" }, { "text": "Virtual Node Graph Neural Network for Full Phonon Prediction: The structure-property relationship plays a central role in materials\nscience. Understanding the structure-property relationship in solid-state\nmaterials is crucial for structure design with optimized properties. The past\nfew years witnessed remarkable progress in correlating structures with\nproperties in crystalline materials, such as machine learning methods and\nparticularly graph neural networks as a natural representation of crystal\nstructures. However, significant challenges remain, including predicting\nproperties with complex unit cells input and material-dependent,\nvariable-length output. Here we present the virtual node graph neural network\nto address the challenges. By developing three types of virtual node approaches\n- the vector, matrix, and momentum-dependent matrix virtual nodes, we achieve\ndirect prediction of $\\Gamma$-phonon spectra and full dispersion only using\natomic coordinates as input. We validate the phonon bandstructures on various\nalloy systems, and further build a $\\Gamma$-phonon database containing over\n146,000 materials in the Materials Project. Our work provides an avenue for\nrapid and high-quality prediction of phonon spectra and bandstructures in\ncomplex materials, and enables materials design with superior phonon properties\nfor energy applications. The virtual node augmentation of graph neural networks\nalso sheds light on designing other functional properties with a new level of\nflexibility.", "category": "cond-mat_dis-nn" }, { "text": "On the Dynamics of Glassy Systems: Glassy systems are disordered systems characterized by extremely slow\ndynamics. Examples are supercooled liquids, whose dynamics slow down under\ncooling. The specific pattern of slowing-down depends on the material\nconsidered. This dependence is poorly understood, in particular, it remains\ngenerally unclear which aspects of the microscopic structures control the\ndynamics and other macroscopic properties. Attacking this question is one of\nthe two main aspects of this dissertation. We have introduced a new class of\nmodels of supercooled liquids, which captures the central aspects of the\ncorrespondence between structure and elasticity on the one hand, the\ncorrelation of structure and thermodynamic and dynamic properties on the other.\nOur results shed new light on the temperature-dependence of the topology of\ncovalent networks, in particular, on the rigidity transition that occurs when\nthe valence is increased.\n Other questions appear in glassy systems at zero temperature. In that\nsituation, a glassy system can flow if an external driving force is imposed\nabove some threshold. The first example we will consider is the erosion of a\nriverbed. Experiments support the existence of a threshold forcing, below which\nno erosion flux is observed. In this dissertation, we present a novel\nmicroscopic model to describe the erosion near threshold. This model makes new\nquantitative predictions for the spatial reparation of the flux. To study\nfurther the self-organization of driven glassy systems, we investigate the\nathermal dynamics of mean-field spin glasses. The spin glass self-organizes\ninto the configurations that are stable, but barely so. Such marginal stability\nappears with the presence of a pseudogap in soft excitations. We show that the\nemergence of a pseudogap is deeply related to very strong anti-correlations\nemerging among soft excitations.", "category": "cond-mat_dis-nn" }, { "text": "Critical properties of the Anderson localization transition and the high\n dimensional limit: In this paper we present a thorough study of transport, spectral and\nwave-function properties at the Anderson localization critical point in spatial\ndimensions $d = 3$, $4$, $5$, $6$. Our aim is to analyze the dimensional\ndependence and to asses the role of the $d\\rightarrow \\infty$ limit provided by\nBethe lattices and tree-like structures. Our results strongly suggest that the\nupper critical dimension of Anderson localization is infinite. Furthermore, we\nfind that the $d_U=\\infty$ is a much better starting point compared to $d_L=2$\nto describe even three dimensional systems. We find that critical properties\nand finite size scaling behavior approach by increasing $d$ the ones found for\nBethe lattices: the critical state becomes an insulator characterized by\nPoisson statistics and corrections to the thermodynamics limit become\nlogarithmic in $N$. In the conclusion, we present physical consequences of our\nresults, propose connections with the non-ergodic delocalised phase suggested\nfor the Anderson model on infinite dimensional lattices and discuss\nperspectives for future research studies.", "category": "cond-mat_dis-nn" }, { "text": "Linear theory of random textures of 3He-A in aerogel: Spacial variation of the orbital part of the order parameter of $^3$He-A in\naerogel is represented as a random walk of the unit vector $\\mathbf{l}$ in a\nfield of random anisotropy produced by the strands of aerogel. For a range of\ndistances, where variation of $\\mathbf{l}$ is small in comparison with its\nabsolute value correlation function of directions of $\\mathbf{l}(\\mathbf{r})$\nis expressed in terms of the correlation function of the random anisotropy\nfield. With simplifying assumptions about this correlation function a spatial\ndependence of the average variation $\\langle\\delta\\mathbf{l}^2\\rangle$ is found\nanalytically for isotropic and axially anisotropic aerogels. Average\nprojections of $\\mathbf{l}$ on the axes of anisotropy are expressed in terms of\ncharacteristic parameters of the problem. Within the \"model of random\ncylinders\" numerical estimations of characteristic length for disruption of the\nlong-range order and of the critical anisotropy for restoration of this order\nare made and compared with other estimations .", "category": "cond-mat_dis-nn" }, { "text": "KPZ equation in one dimension and line ensembles: For suitably discretized versions of the Kardar-Parisi-Zhang equation in one\nspace dimension exact scaling functions are available, amongst them the\nstationary two-point function. We explain one central piece from the technology\nthrough which such results are obtained, namely the method of line ensembles\nwith purely entropic repulsion.", "category": "cond-mat_dis-nn" }, { "text": "Structure and Time-Evolution of an Internet Dating Community: We present statistics for the structure and time-evolution of a network\nconstructed from user activity in an Internet community. The vastness and\nprecise time resolution of an Internet community offers unique possibilities to\nmonitor social network formation and dynamics. Time evolution of well-known\nquantities, such as clustering, mixing (degree-degree correlations), average\ngeodesic length, degree, and reciprocity is studied. In contrast to earlier\nanalyses of scientific collaboration networks, mixing by degree between\nvertices is found to be disassortative. Furthermore, both the evolutionary\ntrajectories of the average geodesic length and of the clustering coefficients\nare found to have minima.", "category": "cond-mat_dis-nn" }, { "text": "Epidemic spread in weighted networks: We study the detailed epidemic spreading process in scale-free networks with\nweight that denote familiarity between two people or computers. The result\nshows that spreading velocity reaches a peak quickly then decays representing\npower-law time behavior, and comparing to non-weighted networks, precise\nhierarchical dynamics is not found although the nodes with larger strength is\npreferential to be infected.", "category": "cond-mat_dis-nn" }, { "text": "Structural Probe of a Glass Forming Liquid: Generalized Compressibility: We introduce a new quantity to probe the glass transition. This quantity is a\nlinear generalized compressibility which depends solely on the positions of the\nparticles. We have performed a molecular dynamics simulation on a glass forming\nliquid consisting of a two component mixture of soft spheres in three\ndimensions. As the temperature is lowered (or as the density is increased), the\ngeneralized compressibility drops sharply at the glass transition, with the\ndrop becoming more and more abrupt as the measurement time increases. At our\nlongest measurement times, the drop occurs approximately at the mode coupling\ntemperature $T_C$. The drop in the linear generalized compressibility occurs at\nthe same temperature as the peak in the specific heat. By examining the\ninherent structure energy as a function of temperature, we find that our\nresults are consistent with the kinetic view of the glass transition in which\nthe system falls out of equilibrium. We find no size dependence and no evidence\nfor a second order phase transition though this does not exclude the\npossibility of a phase transition below the observed glass transition\ntemperature. We discuss the relation between the linear generalized\ncompressibility and the ordinary isothermal compressibility as well as the\nstatic structure factor.", "category": "cond-mat_dis-nn" }, { "text": "Validity of the zero-thermodynamic law in off-equilibrium coupled\n harmonic oscillators: In order to describe the thermodynamics of the glassy systems it has been\nrecently introduced an extra parameter also called effective temperature which\ngeneralizes the fluctuation-dissipation theorem (FDT) to systems\noff-equilibrium and supposedly describes thermal fluctuations around the aging\nstate. Here we investigate the applicability of a zero-th law for\nnon-equilibrium glassy systems based on these effective temperatures by\nstudying two coupled subsystems of harmonic oscillators with Monte Carlo\ndynamics. We analyze in detail two types of dynamics: 1) sequential dynamics\nwhere the coupling between the subsystems comes only from the Hamiltonian and\n2) parallel dynamics where there is a further coupling between the subsystems\narising from the dynamics. We show that the coupling described in the first\ncase is not enough to make asymptotically the effective temperatures of two\ninteracting subsystems coincide, the reason being the too small thermal\nconductivity between them in the aging state. This explains why different\ninteracting degrees of freedom in structural glasses may stay at different\neffective temperatures without never mutually thermalizing.", "category": "cond-mat_dis-nn" }, { "text": "Crystal-like Order Stabilizing Glasses: Structural Origin of\n Ultra-stable Metallic Glasses: Glasses are featured with a disordered amorphous structure, being opposite to\ncrystals that are constituted by periodic lattices. In this study we report\nthat the exceptional thermodynamic and kinetic stability of an ultra-stable\nbinary ZrCu metallic glass, fabricated by high-temperature physical vapor\ndeposition, originates from ubiquitous crystal-like medium range order (MRO)\nconstituted by Voronoi polyhedron ordering with well-defined local\ntranslational symmetry beyond nearest atomic neighbors. The crystal-like MRO\nsignificantly improves the thermodynamic and kinetic stability of the glass,\nwhich is in opposition to the conventional wisdom that crystal-like order\ndeteriorates the stability and forming ability of metallic glasses. This study\nunveils the structural origin of ultra-stable metallic glasses and shines a\nlight on the intrinsic correlation of local atomic structure ordering with\nglass transition of metallic glasses.", "category": "cond-mat_dis-nn" }, { "text": "Origin of the Growing Length Scale in M-p-Spin Glass Models: Two versions of the M-p-spin glass model have been studied with the\nMigdal-Kadanoff renormalization group approximation. The model with p=3 and M=3\nhas at mean-field level the ideal glass transition at the Kauzmann temperature\nand at lower temperatures still the Gardner transition to a state like that of\nan Ising spin glass in a field. The model with p=3 and M=2 has only the Gardner\ntransition. In the dimensions studied, d=2,3 and 4, both models behave almost\nidentically, indicating that the growing correlation length as the temperature\nis reduced in these models -- the analogue of the point-to-set length scale --\nis not due to the mechanism postulated in the random first order transition\ntheory of glasses, but is more like that expected on the analogy of glasses to\nthe Ising spin glass in a field.", "category": "cond-mat_dis-nn" }, { "text": "Universality and Deviations in Disordered Systems: We compute the probability of positive large deviations of the free energy\nper spin in mean-field Spin-Glass models. The probability vanishes in the\nthermodynamic limit as $P(\\Delta f) \\propto \\exp[-N^2 L_2(\\Delta f)]$. For the\nSherrington-Kirkpatrick model we find $L_2(\\Delta f)=O(\\Delta f)^{12/5}$ in\ngood agreement with numerical data and with the assumption that typical small\ndeviations of the free energy scale as $N^{1/6}$. For the spherical model we\nfind $L_2(\\Delta f)=O(\\Delta f)^{3}$ in agreement with recent findings on the\nfluctuations of the largest eigenvalue of random Gaussian matrices. The\ncomputation is based on a loop expansion in replica space and the non-gaussian\nbehaviour follows in both cases from the fact that the expansion is divergent\nat all orders. The factors of the leading order terms are obtained resumming\nappropriately the loop expansion and display universality, pointing to the\nexistence of a single universal distribution describing the small deviations of\nany model in the full-Replica-Symmetry-Breaking class.", "category": "cond-mat_dis-nn" }, { "text": "On the Paramagnetic Impurity Concentration of Silicate Glasses from\n Low-Temperature Physics: The concentration of paramagnetic trace impurities in glasses can be\ndetermined via precise SQUID measurements of the sample's magnetization in a\nmagnetic field. However the existence of quasi-ordered structural\ninhomogeneities in the disordered solid causes correlated tunneling currents\nthat can contribute to the magnetization, surprisingly, also at the higher\ntemperatures. We show that taking into account such tunneling systems gives\nrise to a good agreement between the concentrations extracted from SQUID\nmagnetization and those extracted from low-temperature heat capacity\nmeasurements. Without suitable inclusion of such magnetization contribution\nfrom the tunneling currents we find that the concentration of paramagnetic\nimpurities gets considerably over-estimated. This analysis represents a further\npositive test for the structural inhomogeneity theory of the magnetic effects\nin the cold glasses.", "category": "cond-mat_dis-nn" }, { "text": "Large-scale dynamical simulations of the three-dimensional XY spin glass: Large-scale simulations have been performed in the current-driven\nthree-dimensional XY spin glass with resistively-shunted junction dynamics for\nsample sizes up to $64^3$. It is observed that the linear resistivity at low\ntemperatures tends to zero, providing a strong evidence of a finite temperature\nphase-coherence (i.e. spin-glass) transition. Dynamical scaling analysis\ndemonstrates that a perfect collapse of current-voltage data can be achieved.\nThe obtained critical exponents agree with those in equilibrium Monte Carlo\nsimulations, and are compatible with those observed in various experiments on\nhigh-T$_c$ cuprate superconductors. It is suggested that the spin and the\nchirality order simultaneously. A genuine continuous depinning transition is\nfound at zero temperature. For low temperature creep motion, critical exponents\nare evaluated, and a non-Arrhenius creep motion is observed in the low\ntemperature ordered phase. It is proposed that the XY spin glass gives an\neffective description of the transport properties in high-T$_c$ superconductors\nwith d-wave symmetry.", "category": "cond-mat_dis-nn" }, { "text": "$1/f^\u03b1$ noise and generalized diffusion in random Heisenberg spin\n systems: We study the `flux noise' spectrum of random-bond quantum Heisenberg spin\nsystems using a real-space renormalization group (RSRG) procedure that accounts\nfor both the renormalization of the system Hamiltonian and of a generic probe\nthat measures the noise. For spin chains, we find that the dynamical structure\nfactor $S_q(f)$, at finite wave-vector $q$, exhibits a power-law behavior both\nat high and low frequencies $f$, with exponents that are connected to one\nanother and to an anomalous dynamical exponent through relations that differ at\n$T = 0$ and $T = \\infty$. The low-frequency power-law behavior of the structure\nfactor is inherited by any generic probe with a finite band-width and is of the\nform $1/f^\\alpha$ with $0.5 < \\alpha < 1$. An analytical calculation of the\nstructure factor, assuming a limiting distribution of the RG flow parameters\n(spin size, length, bond strength) confirms numerical findings. More generally,\nwe demonstrate that this form of the structure factor, at high temperatures, is\na manifestation of anomalous diffusion which directly follows from a\ngeneralized spin-diffusion propagator. We also argue that $1/f$-noise is\nintimately connected to many-body-localization at finite temperatures. In two\ndimensions, the RG procedure is less reliable; however, it becomes convergent\nfor quasi-one-dimensional geometries where we find that one-dimensional\n$1/f^\\alpha$ behavior is recovered at low frequencies; the latter\nconfigurations are likely representative of paramagnetic spin networks that\nproduce $1/f^\\alpha$ noise in SQUIDs.", "category": "cond-mat_dis-nn" }, { "text": "Percolation of optical excitation mediated by near-field interactions: Optical excitation transfer in nanostructured matter has been intensively\nstudied in various material systems for versatile applications. Herein, we\ndiscuss the percolation of optical excitations in randomly organized\nnanostructures caused by optical near-field interactions governed by Yukawa\npotential in a two-dimensional stochastic model. The model results demonstrate\nthe appearance of two phases of percolation of optical excitation as a function\nof the localization degree of near-field interaction. Moreover, it indicates\nsublinear scaling with percolation distance when the light localization is\nstrong. The results provide fundamental insights into optical excitation\ntransfer and will facilitate the design and analysis of nanoscale\nsignal-transfer characteristics.", "category": "cond-mat_dis-nn" }, { "text": "From particles to spins: Eulerian formulation of supercooled liquids and\n glasses: The dynamics of supercooled liquid and glassy systems are usually studied\nwithin the Lagrangian representation, in which the positions and velocities of\ndistinguishable interacting particles are followed. Within this representation,\nhowever, it is difficult to define measures of spatial heterogeneities in the\ndynamics, as particles move in and out of any one given region within long\nenough times. It is also non-transparent how to make connections between the\nstructural glass and the spin glass problems within the Lagrangian formulation.\nWe propose an Eulerian formulation of supercooled liquids and glasses that\nallows for a simple connection between particle and spin systems, and that\npermits the study of dynamical heterogeneities within a fixed frame of\nreference similar to the one used for spin glasses. We apply this framework to\nthe study of the dynamics of colloidal particle suspensions for packing\nfractions corresponding to the supercooled and glassy regimes, which are probed\nvia confocal microscopy.", "category": "cond-mat_dis-nn" }, { "text": "Electronic properties of the 1D Frenkel-Kontorova model: The energy spectra and quantum diffusion of an electron in a 1D\nincommensurate Frenkel-Kontorova (FK) model are studied numerically. We found\nthat the spectral and dynamical properties of electron display quite different\nbehaviors in invariance circle regime and in Cantorus regime. In the former\ncase, it is similar to that of the Harper model, whereas in the latter case, it\nis similar to that of the Fibonacci model. The relationship between spectral\nand transport properties is discussed.", "category": "cond-mat_dis-nn" }, { "text": "Dense Hebbian neural networks: a replica symmetric picture of\n unsupervised learning: We consider dense, associative neural-networks trained with no supervision\nand we investigate their computational capabilities analytically, via a\nstatistical-mechanics approach, and numerically, via Monte Carlo simulations.\nIn particular, we obtain a phase diagram summarizing their performance as a\nfunction of the control parameters such as the quality and quantity of the\ntraining dataset and the network storage, valid in the limit of large network\nsize and structureless datasets. Moreover, we establish a bridge between\nmacroscopic observables standardly used in statistical mechanics and loss\nfunctions typically used in the machine learning. As technical remarks, from\nthe analytic side, we implement large deviations and stability analysis within\nGuerra's interpolation to tackle the not-Gaussian distributions involved in the\npost-synaptic potentials while, from the computational counterpart, we insert\nPlefka approximation in the Monte Carlo scheme, to speed up the evaluation of\nthe synaptic tensors, overall obtaining a novel and broad approach to\ninvestigate neural networks in general.", "category": "cond-mat_dis-nn" }, { "text": "Modal makeup of transmission eigenchannels: Transmission eigenchannels and quasi-normal modes are powerful bases for\ndescribing wave transport and controlling transmission and energy storage in\ndisordered media. Here we elucidate the connection between these approaches by\nexpressing the transmission matrix (TM) at a particular frequency as a sum of\nTMs for individual modes drawn from a broad spectral range. The wide range of\ntransmission eigenvalues and correlation frequencies of eigenchannels of\ntransmission is explained by the increasingly off-resonant excitation of modes\ncontributing to eigenchannels with decreasing transmission and by the phasing\nbetween these contributions.", "category": "cond-mat_dis-nn" }, { "text": "A Wavelet Analysis of Transient Spike Trains of Hodgkin-Huxley Neurons: Transient spike trains consisting of $M$ (= 1 - 5) pulses generated by single\nHodgkin-Huxley (HH) neurons, have been analyzed by using both the continuous\nand discrete wavelet transformations (WT). We have studied effects of\nvariations in the interspike intervals (ISI) of the spikes and effects of\nnoises on the energy distribution and the wavelet entropy, which are expressed\nin terms of the WT expansion coefficients. The results obtained by the WT are\ndiscussed in connection with those obtained by the Fourier transformation.", "category": "cond-mat_dis-nn" }, { "text": "Study of longitudinal fluctuations of the Sherrington-Kirkpatrick model: We study finite-size corrections to the free energy of the\nSherrington-Kirkpatrick spin glass in the low temperature phase. We investigate\nthe role of longitudinal fluctuations in these corrections, neglecting the\ntransverse contribution. In particular, we are interested in the exponent\n$\\alpha$ defined by the relation $f-f_\\infty\\sim N^{-\\alpha}$. We perform both\nan analytical and numerical estimate of the analytical result for $\\alpha$.\nFrom both the approaches we get the result: $\\alpha=0.8$.", "category": "cond-mat_dis-nn" }, { "text": "Thermodynamics of the L\u00e9vy spin glass: We investigate the L\\'evy glass, a mean-field spin glass model with power-law\ndistributed couplings characterized by a divergent second moment. By combining\nextensively many small couplings with a spare random backbone of strong bonds\nthe model is intermediate between the Sherrington-Kirkpatrick and the\nViana-Bray model. A truncated version where couplings smaller than some\nthreshold $\\eps$ are neglected can be studied within the cavity method\ndeveloped for spin glasses on locally tree-like random graphs. By performing\nthe limit $\\eps\\to 0$ in a well-defined way we calculate the thermodynamic\nfunctions within replica symmetry and determine the de Almeida-Thouless line in\nthe presence of an external magnetic field. Contrary to previous findings we\nshow that there is no replica-symmetric spin glass phase. Moreover we determine\nthe leading corrections to the ground-state energy within one-step replica\nsymmetry breaking. The effects due to the breaking of replica symmetry appear\nto be small in accordance with the intuitive picture that a few strong bonds\nper spin reduce the degree of frustration in the system.", "category": "cond-mat_dis-nn" }, { "text": "Bosons in Disordered Optical Potentials: In this work we systematically investigate the condensate properties,\nsuperfluid properties and quantum phase transitions in interacting Bose gases\ntrapped in disordered optical potentials. We numerically solve the Bose-Hubbard\nHamiltonian exactly for different: (a) types of disorder, (b) disorder\nstrengths, and (c) interatomic interactions. The three types of disorder\nstudied are: quasiperiodic disorder, uniform random disorder and random\nspeckle-type disorder. We find that the Bose glass, as identified by Fisher et\nal [Phys. Rev. B {\\bf 40}, 546 (1989)], contains a normal condensate component\nand we show how the three different factors listed above affect it.", "category": "cond-mat_dis-nn" }, { "text": "Diffusion of a particle in the Gaussian random energy landscape:\n Einstein relation and analytical properties of average velocity and\n diffusivity as functions of driving force: We demonstrate that the Einstein relation for the diffusion of a particle in\nthe random energy landscape with the Gaussian density of states is an exclusive\n1D property and does not hold in higher dimensions. We also consider the\nanalytical properties of the particle velocity and diffusivity for the limit of\nweak driving force and establish connection between these properties and\ndimensionality and spatial correlation of the random energy landscape.", "category": "cond-mat_dis-nn" }, { "text": "Interaction-Driven Instabilities in the Random-Field XXZ Chain: Despite enormous efforts devoted to the study of the many-body localization\n(MBL) phenomenon, the nature of the high-energy behavior of the Heisenberg spin\nchain in a strong random magnetic field is lacking consensus. Here, we take a\nstep back by exploring the weak interaction limit starting from the Anderson\nlocalized (AL) insulator. Through shift-invert diagonalization, we find that\nbelow a certain disorder threshold $h^*$, weak interactions necessarily lead to\nergodic instability, whereas at strong disorder the AL insulator directly turns\ninto MBL. This agrees with a simple interpretation of the avalanche theory for\nrestoration of ergodicity. We further map the phase diagram for the generic XXZ\nmodel in the disorder $h$ -- interaction $\\Delta$ plane. Taking advantage of\nthe total magnetization conservation, our results unveil the remarkable\nbehavior of the spin-spin correlation functions: in the regime indicated as MBL\nby standard observables, their exponential decay undergoes a unique inversion\nof orientation $\\xi_z>\\xi_x$. We find that the longitudinal length $\\xi_z$ is a\nkey quantity for capturing ergodic instabilities, as it increases with system\nsize near the thermal phase, in sharp contrast to its transverse counterpart\n$\\xi_x$.", "category": "cond-mat_dis-nn" }, { "text": "Statistical properties of localisation--delocalisation transition in one\n dimension: We study a one-dimensional model of disordered electrons (also relevant for\nrandom spin chains), which exhibits a delocalisation transition at\nhalf-filling. Exact probability distribution functions for the Wigner time and\ntransmission coefficient are calculated. We identify and distinguish those\nfeatures of probability densities that are due to rare, trapping configurations\nof the random potential from those which are due to the proximity to the\ndelocalisation transition.", "category": "cond-mat_dis-nn" }, { "text": "Finite-size scaling with respect to interaction and disorder strength at\n the many-body localization transition: We present a finite-size scaling for both interaction and disorder strengths\nin the critical regime of the many-body localization (MBL) transition for a\nspin-1/2 XXZ spin chain with a random field by studying level statistics. We\nshow how the dynamical transition from the thermal to MBL phase depends on\ninteraction together with disorder by evaluating the ratio of adjacent level\nspacings, and thus, extend previous studies in which interaction coupling is\nfixed. We introduce an extra critical exponent in order to describe the\nnontrivial interaction dependence of the MBL transition. It is characterized by\nthe ratio of the disorder strength to the power of the interaction coupling\nwith respect to the extra critical exponent and not by the simple ratio between\nthem.", "category": "cond-mat_dis-nn" }, { "text": "Rare regions and avoided quantum criticality in disordered Weyl\n semimetals and superconductors: Disorder in Weyl semimetals and superconductors is surprisingly subtle,\nattracting attention and competing theories in recent years. In this brief\nreview, we discuss the current theoretical understanding of the effects of\nshort-ranged, quenched disorder on the low energy-properties of\nthree-dimensional, topological Weyl semimetals and superconductors. We focus on\nthe role of non-perturbative rare region effects on destabilizing the semimetal\nphase and rounding the expected semimetal-to-diffusive metal transition into a\ncross over. Furthermore, the consequences of disorder on the resulting nature\nof excitations, transport, and topology are reviewed. New results on a\nbipartite random hopping model are presented that confirm previous results in a\n$p+ip$ Weyl superconductor, demonstrating that particle-hole symmetry is\ninsufficient to help stabilize the Weyl semimetal phase in the presence of\ndisorder. The nature of the avoided transition in a model for a single Weyl\ncone in the continuum is discussed. We close with a discussion of open\nquestions and future directions.", "category": "cond-mat_dis-nn" }, { "text": "One step RSB scheme for the rate distortion function: We apply statistical mechanics to an inverse problem of linear mapping to\ninvestigate the physics of the irreversible compression. We use the replica\nsymmetry breaking (RSB) technique with a toy model to demonstrate the Shannon's\nresult. The rate distortion function, which is widely known as the theoretical\nlimit of the compression with a fidelity criterion, is derived using the Parisi\none step RSB scheme. The bound can not be achieved in the sparsely-connected\nsystems, where suboptimal solutions dominate the capacity.", "category": "cond-mat_dis-nn" }, { "text": "On reducing Terrorism Power: A Hint from Physics: The September 11 attack on the US has revealed an unprecedented terrorism\nworldwide range of destruction. Recently, it has been related to the\npercolation of worldwide spread passive supporters. This scheme puts the\nsuppression of the percolation effect as the major strategic issue in the fight\nagainst terrorism. Accordingly the world density of passive supporters should\nbe reduced below the percolation threshold. In terms of solid policy, it means\nto neutralize millions of random passive supporters, which is contrary to\nethics and out of any sound practical scheme. Given this impossibility we\nsuggest instead a new strategic scheme to act directly on the value of the\nterrorism percolation threshold itself without harming the passive supporters.\nAccordingly we identify the space hosting the percolation phenomenon to be a\nmulti-dimensional virtual social space which extends the ground earth surface\nto include the various independent terrorist-fighting goals. The associated\npercolating cluster is then found to create long-range ground connections to\nterrorism activity. We are thus able to modify the percolation threshold pc in\nthe virtual space to reach p=2 equally\nprobable variants of signal (state of node in Kauffman network) as\ninterpretively based new statistical mechanism (RSN) instead of the bias p -\nprobability of one of signal variants used in RBN family and RNS. It is also\ndifferent than RWN model. For this mechanism which can be treated as very\nfrequent, ordered phase occurs only in exceptional cases but for this approach\nthe chaotic phase is investigated. Annealed approximation expectations and\nsimulations of damage spreading for different network types (similar to CRBN,\nFSRBN and EFRBN but with s>=2) are described. Degree of order in chaotic phase\nin dependency of network parameters and type is discussed. By using such order\nlife evolve. 3- A simplified algorithm called `reversed-annealed' for\nstatistical simulation of damage spreading is described. It is used for\nsimulations presented in this and next papers describing my approach.", "category": "cond-mat_dis-nn" }, { "text": "Bias driven coherent carrier dynamics in a two-dimensional aperiodic\n potential: We study the dynamics of an electron wave-packet in a two-dimensional square\nlattice with an aperiodic site potential in the presence of an external uniform\nelectric field. The aperiodicity is described by $\\epsilon_{\\bf m} =\nV\\cos{(\\pi\\alpha m_x^{\\nu_x})}\\cos{(\\pi\\alpha m_y^{\\nu_y})}$ at lattice sites\n$(m_x, m_y)$, with $\\pi \\alpha$ being a rational number, and $\\nu_x$ and\n$\\nu_y$ tunable parameters, controlling the aperiodicity. Using an exact\ndiagonalization procedure and a finite-size scaling analysis, we show that in\nthe weakly aperiodic regime ($\\nu_x,\\nu_y < 1$), a phase of extended states\nemerges in the center of the band at zero field giving support to a macroscopic\nconductivity in the thermodynamic limit. Turning on the field gives rise to\nBloch oscillations of the electron wave-packet. The spectral density of these\noscillations may display a double peak structure signaling the spatial\nanisotropy of the potential landscape. The frequency of the oscillations can be\nunderstood using a semi-classical approach.", "category": "cond-mat_dis-nn" }, { "text": "Unraveling the nature of carrier mediated ferromagnetism in diluted\n magnetic semiconductors: After more than a decade of intensive research in the field of diluted\nmagnetic semiconductors (DMS), the nature and origin of ferromagnetism,\nespecially in III-V compounds is still controversial. Many questions and open\nissues are under intensive debates. Why after so many years of investigations\nMn doped GaAs remains the candidate with the highest Curie temperature among\nthe broad family of III-V materials doped with transition metal (TM) impurities\n? How can one understand that these temperatures are almost two orders of\nmagnitude larger than that of hole doped (Zn,Mn)Te or (Cd,Mn)Se? Is there any\nintrinsic limitation or is there any hope to reach in the dilute regime room\ntemperature ferromagnetism? How can one explain the proximity of (Ga,Mn)As to\nthe metal-insulator transition and the change from\nRuderman-Kittel-Kasuya-Yosida (RKKY) couplings in II-VI compounds to double\nexchange type in (Ga,Mn)N? In spite of the great success of density functional\ntheory based studies to provide accurately the critical temperatures in various\ncompounds, till very lately a theory that provides a coherent picture and\nunderstanding of the underlying physics was still missing. Recently, within a\nminimal model it has been possible to show that among the physical parameters,\nthe key one is the position of the TM acceptor level. By tuning the value of\nthat parameter, one is able to explain quantitatively both magnetic and\ntransport properties in a broad family of DMS. We will see that this minimal\nmodel explains in particular the RKKY nature of the exchange in\n(Zn,Mn)Te/(Cd,Mn)Te and the double exchange type in (Ga,Mn)N and simultaneously\nthe reason why (Ga,Mn)As exhibits the highest critical temperature among both\nII-VI and III-V DMS.", "category": "cond-mat_dis-nn" }, { "text": "Absorption spectrum of a one-dimensional chain with Frenkel's exciton\n under diagonal disorder represented by hyperbolic defects: A method is proposed for calculating the absorption spectrum of a long\none-dimensional closed-into-a-ring chain with Frenkel's exciton under diagonal\ndisorder. This disorder is represented by the hyperbolic singularities of\natomic fission. These defects are shown to lead to a wing in the exciton zone\nof a chain without defects. The form of the wing does not depend on the\nrelative positions or number of defects and its value is proportional to the\nsum of the amplitudes of the defects. The proposed method uses only the\ncontinual approximation.", "category": "cond-mat_dis-nn" }, { "text": "Disorder Induced Anomalous Hall Effect in Type-I Weyl Metals: Connection\n between the Kubo-Streda Formula in the Spin and Chiral basis: We study the anomalous Hall effect (AHE) in tilted Weyl metals with weak\nGaussian disorder under the Kubo-Streda formalism in this work. To separate the\nthree different contributions, namely the intrinsic, side jump and skew\nscattering contribution, it is usually considered necessary to go to the\neigenstate (chiral) basis of the Kubo-Streda formula. However, it is more\nstraight-forward to compute the total Hall current in the spin basis. For the\nreason, we develop a systematic and transparent scheme to separate the three\ndifferent contributions in the spin basis for relativistic systems by building\na one-to-one correspondence between the Feynman diagrams of the different\nmechanisms in the chiral basis and the products of the symmetric and\nanti-symmetric part of the polarization operator in the spin basis. We obtain\nthe three contributions of the AHE in tilted Weyl metals by this scheme and\nfound that the side jump contribution exceeds both the intrinsic and skew\nscattering contribution for the low-energy effective Hamiltonian. We compared\nthe anomalous Hall current obtained from our scheme with the results from the\nsemi-classical Boltzmann equation approach under the relaxation time\napproximation and found that the results from the two approaches agree with\neach other in the leading order of the tilting velocity.", "category": "cond-mat_dis-nn" }, { "text": "Energy-Efficient and Robust Associative Computing with Electrically\n Coupled Dual Pillar Spin-Torque Oscillators: Dynamics of coupled spin-torque oscillators can be exploited for non-Boolean\ninformation processing. However, the feasibility of coupling large number of\nSTOs with energy-efficiency and sufficient robustness towards\nparameter-variation and thermal-noise, may be critical for such computing\napplications. In this work, the impacts of parameter-variation and\nthermal-noise on two different coupling mechanisms for STOs, namely,\nmagnetic-coupling and electrical-coupling are analyzed. Magnetic coupling is\nsimulated using dipolar-field interactions. For electricalcoupling we employed\nglobal RF-injection. In this method, multiple STOs are phase-locked to a common\nRF-signal that is injected into the STOs along with the DC bias. Results for\nvariation and noise analysis indicate that electrical-coupling can be\nsignificantly more robust as compared to magnetic-coupling. For\nroom-temperature simulations, appreciable phase-lock was retained among tens of\nelectrically coupled STOs for up to 20% 3s random variations in critical device\nparameters. The magnetic-coupling technique however failed to retain locking\nbeyond ~3% 3s parameter-variations, even for small-size STO clusters with\nnear-neighborhood connectivity. We propose and analyze Dual-Pillar STO (DP-STO)\nfor low-power computing using the proposed electrical coupling method. We\nobserved that DP-STO can better exploit the electrical-coupling technique due\nto separation between the biasing RF signal and its own RF output.", "category": "cond-mat_dis-nn" }, { "text": "The integrated density of states of the random graph Laplacian: We analyse the density of states of the random graph Laplacian in the\npercolating regime. A symmetry argument and knowledge of the density of states\nin the nonpercolating regime allows us to isolate the density of states of the\npercolating cluster (DSPC) alone, thereby eliminating trivially localised\nstates due to finite subgraphs. We derive a nonlinear integral equation for the\nintegrated DSPC and solve it with a population dynamics algorithm. We discuss\nthe possible existence of a mobility edge and give strong evidence for the\nexistence of discrete eigenvalues in the whole range of the spectrum.", "category": "cond-mat_dis-nn" }, { "text": "Localized Modes in Open One-Dimensional Dissipative Random Systems: We consider, both theoretically and experimentally, the excitation and\ndetection of the localized quasi-modes (resonances) in an open dissipative 1D\nrandom system. We show that even though the amplitude of transmission drops\ndramatically so that it cannot be observed in the presence of small losses,\nresonances are still clearly exhibited in reflection. Surprisingly, small\nlosses essentially improve conditions for the detection of resonances in\nreflection as compared with the lossless case. An algorithm is proposed and\ntested to retrieve sample parameters and resonances characteristics inside the\nrandom system exclusively from reflection measurements.", "category": "cond-mat_dis-nn" }, { "text": "Level spacing distribution of localized phases induced by quasiperiodic\n potentials: Level statistics is a crucial tool in the exploration of localization\nphysics. The level spacing distribution of the disordered localized phase\nfollows Poisson statistics, and many studies naturally apply it to the\nquasiperiodic localized phase. Here we analytically obtain the level spacing\ndistribution of the quasiperiodic localized phase, and find that it deviates\nfrom Poisson statistics. Moreover, based on this level statistics, we derive\nthe ratio of adjacent gaps and find that for a single sample, it is a $\\delta$\nfunction, which is in excellent agreement with numerical studies. Additionally,\nunlike disordered systems, in quasiperiodic systems, there are variations in\nthe level spacing distribution across different regions of the spectrum, and\nincreasing the size and increasing the sample are non-equivalent. Our findings\ncarry significant implications for the reevaluation of level statistics in\nquasiperiodic systems and a profound understanding of the distinct effects of\nquasiperiodic potentials and disorder induced localization.", "category": "cond-mat_dis-nn" }, { "text": "Geometry, Topology and Simplicial Synchronization: Simplicial synchronization reveals the role that topology and geometry have\nin determining the dynamical properties of simplicial complexes. Simplicial\nnetwork geometry and topology are naturally encoded in the spectral properties\nof the graph Laplacian and of the higher-order Laplacians of simplicial\ncomplexes. Here we show how the geometry of simplicial complexes induces\nspectral dimensions of the simplicial complex Laplacians that are responsible\nfor changing the phase diagram of the Kuramoto model. In particular, simplicial\ncomplexes displaying a non-trivial simplicial network geometry cannot sustain a\nsynchronized state in the infinite network limit if their spectral dimension is\nsmaller or equal to four. This theoretical result is here verified on the\nNetwork Geometry with Flavor simplicial complex generative model displaying\nemergent hyperbolic geometry. On its turn simplicial topology is shown to\ndetermine the dynamical properties of the higher-order Kuramoto model. The\nhigher-orderKuramoto model describes synchronization of topological signals,\ni.e. phases not only associated to the nodes of a simplicial complexes but\nassociated also to higher-order simplices, including links, triangles and so\non. This model displays discontinuous synchronization transitions when\ntopological signals of different dimension and/or their solenoidal and\nirrotational projections are coupled in an adaptive way.", "category": "cond-mat_dis-nn" }, { "text": "Many-Body Localization: Transitions in Spin Models: We study the transitions between ergodic and many-body localized phases in\nspin systems, subject to quenched disorder, including the Heisenberg chain and\nthe central spin model. In both cases systems with common spin lengths $1/2$\nand $1$ are investigated via exact numerical diagonalization and random matrix\ntechniques.\n Particular attention is paid to the sample-to-sample variance $(\\Delta_sr)^2$\nof the averaged consecutive-gap ratio $\\langle r\\rangle$ for different disorder\nrealizations. For both types of systems and spin lengths we find a maximum in\n$\\Delta_sr$ as a function of disorder strength, accompanied by an inflection\npoint of $\\langle r\\rangle$, signaling the transition from ergodicity to\nmany-body localization. The critical disorder strength is found to be somewhat\nsmaller than the values reported in the recent literature.\n Further information about the transitions can be gained from the probability\ndistribution of expectation values within a given disorder realization.", "category": "cond-mat_dis-nn" }, { "text": "Full solution for the storage of correlated memories in an\n autoassociative memory: We complement our previous work [arxiv: 0707.0565] with the full (non\ndiluted) solution describing the stable states of an attractor network that\nstores correlated patterns of activity. The new solution provides a good fit of\nsimulations of a network storing the feature norms of McRae and colleagues\n[McRae et al, 2005], experimentally obtained combinations of features\nrepresenting concepts in semantic memory. We discuss three ways to improve the\nstorage capacity of the network: adding uninformative neurons, removing\ninformative neurons and introducing popularity-modulated hebbian learning. We\nshow that if the strength of synapses is modulated by an exponential decay of\nthe popularity of the pre-synaptic neuron, any distribution of patterns can be\nstored and retrieved with approximately an optimal storage capacity - i.e, C ~\nI.p, the minimum number of connections per neuron needed to sustain the\nretrieval of a pattern is proportional to the information content of the\npattern multiplied by the number of patterns stored in the network.", "category": "cond-mat_dis-nn" }, { "text": "Generic Modeling of Chemotactic Based Self-Wiring of Neural Networks: The proper functioning of the nervous system depends critically on the\nintricate network of synaptic connections that are generated during the system\ndevelopment. During the network formation, the growth cones migrate through the\nembryonic environment to their targets using chemical communication. A major\nobstacle in the elucidation of fundamental principles underlying this\nself-wiring is the complexity of the system being analyzed. Hence much effort\nis devoted to in-vitro experiments of simpler 2D model systems. In these\nexperiments neurons are placed on Poly-L-Lysine (PLL) surfaces so it is easier\nto monitor their self-wiring. We developed a model to reproduce the salient\nfeatures of the 2D systems, inspired by the study of bacterial colony's growth\nand the aggregation of amoebae. We represent the neurons (each composed of\ncell's soma, neurites and growth cones) by active elements that capture the\ngeneric features of the real neurons. The model also incorporates stationary\nunits representing the cells' soma and communicating walkers representing the\ngrowth cones. The stationary units send neurites one at a time, and respond to\nchemical signaling. The walkers migrate in response to chemotaxis substances\nemitted by the soma and communicate with each other and with the soma by means\nof chemotactic ``feedback''. The interplay between the chemo-repulsive and\nchemo-attractive responses is determined by the dynamics of the walker's\ninternal energy which is controlled by the soma. These features enable the\nneurons to perform the complex task of self-wiring.", "category": "cond-mat_dis-nn" }, { "text": "Surface properties at the Kosterlitz-Thouless transition: Monte Carlo simulations of the two-dimensional XY model are performed in a\nsquare geometry with free and mixed fixed-free boundary conditions. Using a\nSchwarz-Christoffel conformal mapping, we deduce the exponent eta of the order\nparameter correlation function and its surface equivalent eta_parallel at the\nKosterlitz-Thouless transition temperature. The well known value eta(T_{KT}) =\n1/4 is easily recovered even with systems of relatively small sizes, since the\nshape effects are encoded in the conformal mapping. The exponent associated to\nthe surface correlations is similarly obtained eta_1(T_{KT}) ~= 0.54.", "category": "cond-mat_dis-nn" }, { "text": "Application of Polynomial Algorithms to a Random Elastic Medium: A randomly pinned elastic medium in two dimensions is modeled by a disordered\nfully-packed loop model. The energetics of disorder-induced dislocations is\nstudied using exact and polynomial algorithms from combinatorial optimization.\nDislocations are found to become unbound at large scale, and the elastic phase\nis thus unstable giving evidence for the absence of a Bragg glass in two\ndimensions.", "category": "cond-mat_dis-nn" }, { "text": "Broken Replica Symmetry Bounds in the Mean Field Spin Glass Model: By using a simple interpolation argument, in previous work we have proven the\nexistence of the thermodynamic limit, for mean field disordered models,\nincluding the Sherrington-Kirkpatrick model, and the Derrida p-spin model. Here\nwe extend this argument in order to compare the limiting free energy with the\nexpression given by the Parisi Ansatz, and including full spontaneous replica\nsymmetry breaking. Our main result is that the quenched average of the free\nenergy is bounded from below by the value given in the Parisi Ansatz uniformly\nin the size of the system. Moreover, the difference between the two expressions\nis given in the form of a sum rule, extending our previous work on the\ncomparison between the true free energy and its replica symmetric\nSherrington-Kirkpatrick approximation. We give also a variational bound for the\ninfinite volume limit of the ground state energy per site.", "category": "cond-mat_dis-nn" }, { "text": "Quantized Repetitions of the Cuprate Pseudogap Line: The cuprate superconductors display several characteristic temperatures which\ndecrease as the material composition is doped, tracing lines across the\ntemperature-doping phase diagram. Foremost among these is the pseudogap\ntransition. At a higher temperature a peak is seen in the magnetic\nsusceptibility, and changes in symmetry and in transport are seen at other\ncharacteristic temperatures. We report a meta-analysis of all measurements of\ncharacteristic temperatures well above $T_c$ in strontium doped lanthanum\ncuprate (LSCO) and oxygen doped YBCO. The experimental corpus shows that the\npseudogap line is one of a family of four straight lines which stretches across\nthe phase diagram from low to high doping, and from $T_c$ up to $700$ K. These\nlines all originate from a single point near the overdoped limit of the\nsuperconducting phase and increase as doping is reduced. The slope of the\npseudogap lines is quantized, with the second, third, and fourth lines having\nslopes that are respectively $1/2,\\;1/3,$ and $1/4$ of the slope of the highest\nline. This pattern suggests that the cuprates host a single mother phase\ncontrolled by a 2-D sheet density which is largest at zero doping and which\ndecreases linearly with hole density, and that the pseudogap lines, charge\ndensity wave order, and superconductivity are all subsidiary effects supported\nby the mother phase.", "category": "cond-mat_dis-nn" }, { "text": "Long Range Order at Low Temperature in Dipolar Spin Ice: Recently it has been suggested that long range magnetic dipolar interactions\nare responsible for spin ice behavior in the Ising pyrochlore magnets ${\\rm\nDy_{2}Ti_{2}O_{7}}$ and ${\\rm Ho_{2}Ti_{2}O_{7}}$. We report here numerical\nresults on the low temperature properties of the dipolar spin ice model,\nobtained via a new loop algorithm which greatly improves the dynamics at low\ntemperature. We recover the previously reported missing entropy in this model,\nand find a first order transition to a long range ordered phase with zero total\nmagnetization at very low temperature. We discuss the relevance of these\nresults to ${\\rm Dy_{2}Ti_{2}O_{7}}$ and ${\\rm Ho_{2}Ti_{2}O_{7}}$.", "category": "cond-mat_dis-nn" }, { "text": "Storage properties of a quantum perceptron: Driven by growing computational power and algorithmic developments, machine\nlearning methods have become valuable tools for analyzing vast amounts of data.\nSimultaneously, the fast technological progress of quantum information\nprocessing suggests employing quantum hardware for machine learning purposes.\nRecent works discuss different architectures of quantum perceptrons, but the\nabilities of such quantum devices remain debated. Here, we investigate the\nstorage capacity of a particular quantum perceptron architecture by using\nstatistical mechanics techniques and connect our analysis to the theory of\nclassical spin glasses. We focus on a specific quantum perceptron model and\nexplore its storage properties in the limit of a large number of inputs.\nFinally, we comment on using statistical physics techniques for further studies\nof neural networks.", "category": "cond-mat_dis-nn" }, { "text": "Viscosity and relaxation processes of the liquid become amorphous\n Al-Ni-REM alloys: The temperature and time dependencies of viscosity of the liquid alloys,\nAl87Ni8Y5, Al86Ni8La6, Al86Ni8Ce6, and the binary Al-Ni and Al-Y melts with Al\nconcentration over 90 at.% have been studied. Non-monotonic relaxation\nprocesses caused by destruction of nonequilibrium state inherited from the\nbasic-heterogeneous alloy have been found to take place in Al-Y, Al-Ni-REM\nmelts after the phase solid-liquid transition. The mechanism of nonmonotonic\nrelaxation in non-equilibrium melts has been suggested.", "category": "cond-mat_dis-nn" }, { "text": "Random Networks of Spiking Neurons: Instability in the Xenopus tadpole\n moto-neural pattern: A large network of integrate-and-fire neurons is studied analytically when\nthe synaptic weights are independently randomly distributed according to a\nGaussian distribution with arbitrary mean and variance. The relevant order\nparameters are identified, and it is shown that such network is statistically\nequivalent to an ensemble of independent integrate-and-fire neurons with each\ninput signal given by the sum of a self-interaction deterministic term and a\nGaussian colored noise. The model is able to reproduce the quasi-synchronous\noscillations, and the dropout of their frequency, of the central nervous system\nneurons of the swimming Xenopus tadpole. Predictions from the model are\nproposed for future experiments.", "category": "cond-mat_dis-nn" }, { "text": "The Hidden Landscape of Localization: Wave localization occurs in all types of vibrating systems, in acoustics,\nmechanics, optics, or quantum physics. It arises either in systems of irregular\ngeometry (weak localization) or in disordered systems (Anderson localization).\nWe present here a general theory that explains how the system geometry and the\nwave operator interplay to give rise to a \"landscape\" that splits the system\ninto weakly coupled subregions, and how these regions shape the spatial\ndistribution of the vibrational eigenmodes. This theory holds in any dimension,\nfor any domain shape, and for all operators deriving from an energy form. It\nencompasses both weak and Anderson localizations in the same mathematical frame\nand shows, in particular, that Anderson localization can be understood as a\nspecial case of weak localization in a very rough landscape.", "category": "cond-mat_dis-nn" }, { "text": "Multifractality and self-averaging at the many-body localization\n transition: Finite-size effects have been a major and justifiable source of concern for\nstudies of many-body localization, and several works have been dedicated to the\nsubject. In this paper, however, we discuss yet another crucial problem that\nhas received much less attention, that of the lack of self-averaging and the\nconsequent danger of reducing the number of random realizations as the system\nsize increases. By taking this into account and considering ensembles with a\nlarge number of samples for all system sizes analyzed, we find that the\ngeneralized dimensions of the eigenstates of the disordered Heisenberg spin-1/2\nchain close to the transition point to localization are described remarkably\nwell by an exact analytical expression derived for the non-interacting\nFibonacci lattice, thus providing an additional tool for studies of many-body\nlocalization.", "category": "cond-mat_dis-nn" }, { "text": "Asymptotically exact theory for nonlinear spectroscopy of random quantum\n magnets: We study nonlinear response in quantum spin systems {near infinite-randomness\ncritical points}. Nonlinear dynamical probes, such as two-dimensional (2D)\ncoherent spectroscopy, can diagnose the nearly localized character of\nexcitations in such systems. {We present exact results for nonlinear response\nin the 1D random transverse-field Ising model, from which we extract\ninformation about critical behavior that is absent in linear response. Our\nanalysis yields exact scaling forms for the distribution functions of\nrelaxation times that result from realistic channels for dissipation in random\nmagnets}. We argue that our results capture the scaling of relaxation times and\nnonlinear response in generic random quantum magnets in any spatial dimension.", "category": "cond-mat_dis-nn" }, { "text": "Of symmetries, symmetry classes, and symmetric spaces: from disorder and\n quantum chaos to topological insulators: Quantum mechanical systems with some degree of complexity due to multiple\nscattering behave as if their Hamiltonians were random matrices. Such behavior,\nwhile originally surmised for the interacting many-body system of highly\nexcited atomic nuclei, was later discovered in a variety of situations\nincluding single-particle systems with disorder or chaos. A fascinating theme\nin this context is the emergence of universal laws for the fluctuations of\nenergy spectra and transport observables. After an introduction to the basic\nphenomenology, the talk highlights the role of symmetries for universality, in\nparticular the correspondence between symmetry classes and symmetric spaces\nthat led to a classification scheme dubbed the 'Tenfold Way'. Perhaps\nsurprisingly, the same scheme has turned out to organize also the world of\ntopological insulators.", "category": "cond-mat_dis-nn" }, { "text": "Minimal contagious sets in random regular graphs: The bootstrap percolation (or threshold model) is a dynamic process modelling\nthe propagation of an epidemic on a graph, where inactive vertices become\nactive if their number of active neighbours reach some threshold. We study an\noptimization problem related to it, namely the determination of the minimal\nnumber of active sites in an initial configuration that leads to the activation\nof the whole graph under this dynamics, with and without a constraint on the\ntime needed for the complete activation. This problem encompasses in special\ncases many extremal characteristics of graphs like their independence,\ndecycling or domination number, and can also be seen as a packing problem of\nrepulsive particles. We use the cavity method (including the effects of replica\nsymmetry breaking), an heuristic technique of statistical mechanics many\npredictions of which have been confirmed rigorously in the recent years. We\nhave obtained in this way several quantitative conjectures on the size of\nminimal contagious sets in large random regular graphs, the most striking being\nthat 5-regular random graph with a threshold of activation of 3 (resp.\n6-regular with threshold 4) have contagious sets containing a fraction 1/6\n(resp. 1/4) of the total number of vertices. Equivalently these numbers are the\nminimal fraction of vertices that have to be removed from a 5-regular (resp.\n6-regular) random graph to destroy its 3-core. We also investigated Survey\nPropagation like algorithmic procedures for solving this optimization problem\non single instances of random regular graphs.", "category": "cond-mat_dis-nn" }, { "text": "Acoustic Cloak Design via Machine Learning: Acoustic metamaterials are engineered microstructures with special mechanical\nand acoustic properties enabling exotic effects such as wave steering, focusing\nand cloaking. The design of acoustic cloaks using scattering cancellation has\ntraditionally involved the optimization of metamaterial structure based on\ndirect computer simulations of the total scattering cross section (TSCS) for a\nlarge number of configurations. Here, we work with sets of cylindrical objects\nconfined in a region of space and use machine learning methods to streamline\nthe design of 2D configurations of scatterers with minimal TSCS demonstrating\ncloaking effect at discrete sets of wavenumbers. After establishing that\nartificial neural networks are capable of learning the TSCS based on the\nlocation of cylinders, we develop an inverse design algorithm, combining\nvariational autoencoders and the Gaussian process, for predicting optimal\narrangements of scatterers given the TSCS. We show results for up to eight\ncylinders and discuss the efficiency and other advantages of the machine\nlearning approach.", "category": "cond-mat_dis-nn" }, { "text": "Tunneling probe of fluctuating superconductivity in disordered thin\n films: Disordered thin films close to the superconducting-insulating phase\ntransition (SIT) hold the key to understanding quantum phase transition in\nstrongly correlated materials. The SIT is governed by superconducting quantum\nfluctuations, which can be revealed for example by tunneling measurements.\nThese experiments detect a spectral gap, accompanied by suppressed coherence\npeaks that do not fit the BCS prediction. To explain these observations, we\nconsider the effect of finite-range superconducting fluctuations on the density\nof states, focusing on the insulating side of the SIT. We perform a controlled\ndiagrammatic resummation and derive analytic expressions for the tunneling\ndifferential conductance. We find that short-range superconducting fluctuations\nsuppress the coherence peaks, even in the presence of long-range correlations.\nOur approach offers a quantitative description of existing measurements on\ndisordered thin films and accounts for tunneling spectra with suppressed\ncoherence peaks observed, for example, in the pseudo gap regime of\nhigh-temperature superconductors.", "category": "cond-mat_dis-nn" }, { "text": "Finite-size scaling analysis of localization transition for scalar waves\n in a 3D ensemble of resonant point scatterers: We use the random Green's matrix model to study the scaling properties of the\nlocalization transition for scalar waves in a three-dimensional (3D) ensemble\nof resonant point scatterers. We show that the probability density $p(g)$ of\nnormalized decay rates of quasi-modes $g$ is very broad at the transition and\nin the localized regime and that it does not obey a single-parameter scaling\nlaw for finite system sizes that we can access. The single-parameter scaling\nlaw holds, however, for the small-$g$ part of $p(g)$ which we exploit to\nestimate the critical exponent $\\nu$ of the localization transition.\nFinite-size scaling analysis of small-$q$ percentiles $g_q$ of $p(g)$ yields an\nestimate $\\nu \\simeq 1.55 \\pm 0.07$. This value is consistent with previous\nresults for Anderson transition in the 3D orthogonal universality class and\nsuggests that the localization transition under study belongs to the same\nclass.", "category": "cond-mat_dis-nn" }, { "text": "Mixed spectra and partially extended states in a two-dimensional\n quasiperiodic model: We introduce a two-dimensional generalisation of the quasiperiodic\nAubry-Andr\\'e model. Even though this model exhibits the same duality relation\nas the one-dimensional version, its localisation properties are found to be\nsubstantially more complex. In particular, partially extended single-particle\nstates appear for arbitrarily strong quasiperiodic modulation. They are\nconcentrated on a network of low-disorder lattice lines, while the rest of the\nlattice hosts localised states. This spatial separation protects the localised\nstates from delocalisation, so no mobility edge emerges in the spectrum.\nInstead, localised and partially extended states are interspersed, giving rise\nto an unusual type of mixed spectrum and enabling complex dynamics even in the\nabsence of interactions. A striking example is ballistic transport across the\nlow-disorder lines while the rest of the system remains localised. This\nbehaviour is robust against disorder and other weak perturbations. Our model is\nthus directly amenable to experimental studies and promises fascinating\nmany-body localisation properties.", "category": "cond-mat_dis-nn" }, { "text": "How many longest increasing subsequences are there?: We study the entropy $S$ of longest increasing subsequences (LIS), i.e., the\nlogarithm of the number of distinct LIS. We consider two ensembles of\nsequences, namely random permutations of integers and sequences drawn i.i.d.\\\nfrom a limited number of distinct integers. Using sophisticated algorithms, we\nare able to exactly count the number of LIS for each given sequence.\nFurthermore, we are not only measuring averages and variances for the\nconsidered ensembles of sequences, but we sample very large parts of the\nprobability distribution $p(S)$ with very high precision. Especially, we are\nable to observe the tails of extremely rare events which occur with\nprobabilities smaller than $10^{-600}$. We show that the distribution of the\nentropy of the LIS is approximately Gaussian with deviations in the far tails,\nwhich might vanish in the limit of long sequences. Further we propose a\nlarge-deviation rate function which fits best to our observed data.", "category": "cond-mat_dis-nn" }, { "text": "Anisotropic spin relaxation in $n$-GaAs from strong inhomogeneous\n hyperfine fields produced by the dynamical polarization of nuclei: The hyperfine field from dynamically polarized nuclei in n-GaAs is very\nspatially inhomogeneous, as the nu- clear polarization process is most\nefficient near the randomly-distributed donors. Electrons with polarized spins\ntraversing the bulk semiconductor will experience this inhomogeneous hyperfine\nfield as an effective fluctuating spin precession rate, and thus the spin\npolarization of an electron ensemble will relax. A theory of spin relaxation\nbased on the theory of random walks is applied to such an ensemble precessing\nin an oblique magnetic field, and the precise form of the (unequal)\nlongitudinal and transverse spin relaxation analytically derived. To\ninvestigate this mechanism, electrical three-terminal Hanle measurements were\nperformed on epitaxially grown Co$_2$MnSi/$n$-GaAs heterostructures fabricated\ninto electrical spin injection devices. The proposed anisotropic spin\nrelaxation mechanism is required to satisfactorily describe the Hanle\nlineshapes when the applied field is oriented at large oblique angles.", "category": "cond-mat_dis-nn" }, { "text": "Classical Quantum Optimization with Neural Network Quantum States: The classical simulation of quantum systems typically requires exponential\nresources. Recently, the introduction of a machine learning-based wavefunction\nansatz has led to the ability to solve the quantum many-body problem in regimes\nthat had previously been intractable for existing exact numerical methods.\nHere, we demonstrate the utility of the variational representation of quantum\nstates based on artificial neural networks for performing quantum optimization.\nWe show empirically that this methodology achieves high approximation ratio\nsolutions with polynomial classical computing resources for a range of\ninstances of the Maximum Cut (MaxCut) problem whose solutions have been encoded\ninto the ground state of quantum many-body systems up to and including 256\nqubits.", "category": "cond-mat_dis-nn" }, { "text": "Absence of diffusion in certain random lattices: Numerical evidence: We demonstrate, by solving numerically the time-dependent Schroedinger\nequation, the physical character of electron localization in a disordered\ntwo-dimensional lattice. We show, in agreement with the prediction of P. W.\nAnderson, that the disorder prevents electron diffusion. The electron becomes\nspatially localized in a specific area of the system. Our numerical analysis\nconfirms that the electron localization is a quantum effect caused by the wave\ncharacter of electron propagation and has no analogy in classical mechanics.", "category": "cond-mat_dis-nn" }, { "text": "Return probability: Exponential versus Gaussian decay: We analyze, both analytically and numerically, the time-dependence of the\nreturn probability in closed systems of interacting particles. Main attention\nis paid to the interplay between two regimes, one of which is characterized by\nthe Gaussian decay of the return probability, and another one is the well known\nregime of the exponential decay. Our analytical estimates are confirmed by the\nnumerical data obtained for two models with random interaction. In view of\nthese results, we also briefly discuss the dynamical model which was recently\nproposed for the implementation of a quantum computation.", "category": "cond-mat_dis-nn" }, { "text": "One+Infinite Dimensional Attractor Neural Networks: We solve a class of attractor neural network models with a mixture of 1D\nnearest-neighbour and infinite-range interactions, which are of a Hebbian-type\nform. Our solution is based on a combination of mean-field methods, transfer\nmatrices and 1D random-field techniques, and is obtained for Boltzmann-type\nequilibrium (following sequential Glauber dynamics) and Peretto-type\nequilibrium (following parallel dynamics). Competition between the alignment\nforces mediated via short-range interactions, and those mediated via\ninfinite-range ones, is found to generate novel phenomena, such as multiple\nlocally stable `pure' states, first-order transitions between recall states,\n2-cycles and non-recall states, and domain formation leading to extremely long\nrelaxation times. We test our results against numerical simulations and simple\nbenchmark cases and find excellent agreement.", "category": "cond-mat_dis-nn" }, { "text": "Virtual Node Graph Neural Network for Full Phonon Prediction: The structure-property relationship plays a central role in materials\nscience. Understanding the structure-property relationship in solid-state\nmaterials is crucial for structure design with optimized properties. The past\nfew years witnessed remarkable progress in correlating structures with\nproperties in crystalline materials, such as machine learning methods and\nparticularly graph neural networks as a natural representation of crystal\nstructures. However, significant challenges remain, including predicting\nproperties with complex unit cells input and material-dependent,\nvariable-length output. Here we present the virtual node graph neural network\nto address the challenges. By developing three types of virtual node approaches\n- the vector, matrix, and momentum-dependent matrix virtual nodes, we achieve\ndirect prediction of $\\Gamma$-phonon spectra and full dispersion only using\natomic coordinates as input. We validate the phonon bandstructures on various\nalloy systems, and further build a $\\Gamma$-phonon database containing over\n146,000 materials in the Materials Project. Our work provides an avenue for\nrapid and high-quality prediction of phonon spectra and bandstructures in\ncomplex materials, and enables materials design with superior phonon properties\nfor energy applications. The virtual node augmentation of graph neural networks\nalso sheds light on designing other functional properties with a new level of\nflexibility.", "category": "cond-mat_dis-nn" }, { "text": "Synchrony and variability induced by spatially correlated additive and\n multiplicative noise in the coupled Langevin model: The synchrony and variability have been discussed of the coupled Langevin\nmodel subjected to spatially correlated additive and multiplicative noise. We\nhave employed numerical simulations and the analytical augmented-moment method\nwhich is the second-order moment method for local and global variables [H.\nHasegawa, Phys. Rev. E {\\bf 67}, 041903 (2003)]. It has been shown that the\nsynchrony of an ensemble is increased (decreased) by a positive (negative)\nspatial correlation in both additive and multiplicative noise. Although the\nvariability for local fluctuations is almost insensitive to spatial\ncorrelations, that for global fluctuations is increased (decreased) by positive\n(negative) correlations. When a pulse input is applied, the synchrony is\nincreased for the correlated multiplicative noise, whereas it may be decreased\nfor correlated additive noise coexisting with uncorrelated multiplicative\nnoise. An application of our study to neuron ensembles has demonstrated the\npossibility that information is conveyed by the variance and synchrony in input\nsignals, which accounts for some neuronal experiments.", "category": "cond-mat_dis-nn" }, { "text": "Can the dynamics of an atomic glass-forming system be described as a\n continuous time random walk?: We show that the dynamics of supercooled liquids, analyzed from computer\nsimulations of the binary mixture Lennard-Jones system, can be described in\nterms of a continuous time random walk (CTRW). The required discretization\ncomes from mapping the dynamics on transitions between metabasins. This\ncomparison involves verifying the conditions of the CTRW as well as a\nquantitative test of the predictions. In particular it is possible to express\nthe wave vector-dependence of the relaxation time as well as the degree of\nnon-exponentiality in terms of the first three moments of the waiting time\ndistribution.", "category": "cond-mat_dis-nn" }, { "text": "Replacing neural networks by optimal analytical predictors for the\n detection of phase transitions: Identifying phase transitions and classifying phases of matter is central to\nunderstanding the properties and behavior of a broad range of material systems.\nIn recent years, machine-learning (ML) techniques have been successfully\napplied to perform such tasks in a data-driven manner. However, the success of\nthis approach notwithstanding, we still lack a clear understanding of ML\nmethods for detecting phase transitions, particularly of those that utilize\nneural networks (NNs). In this work, we derive analytical expressions for the\noptimal output of three widely used NN-based methods for detecting phase\ntransitions. These optimal predictions correspond to the results obtained in\nthe limit of high model capacity. Therefore, in practice they can, for example,\nbe recovered using sufficiently large, well-trained NNs. The inner workings of\nthe considered methods are revealed through the explicit dependence of the\noptimal output on the input data. By evaluating the analytical expressions, we\ncan identify phase transitions directly from experimentally accessible data\nwithout training NNs, which makes this procedure favorable in terms of\ncomputation time. Our theoretical results are supported by extensive numerical\nsimulations covering, e.g., topological, quantum, and many-body localization\nphase transitions. We expect similar analyses to provide a deeper understanding\nof other classification tasks in condensed matter physics.", "category": "cond-mat_dis-nn" }, { "text": "Interaction corrections to the Hall coefficient at intermediate\n temperatures: We investigate the effect of electron-electron interaction on the temperature\ndependence of the Hall coefficient of 2D electron gas at arbitrary relation\nbetween the temperature $T$ and the elastic mean-free time $\\tau$. At small\ntemperature $T\\tau \\ll \\hbar$ we reproduce the known relation between the\nlogarithmic temperature dependences of the Hall coefficient and of the\nlongitudinal conductivity. At higher temperatures, this relation is violated\nquite rapidly; correction to the Hall coefficient becomes $\\propto 1/T$ whereas\nthe longitudinal conductivity becomes linear in temperature.", "category": "cond-mat_dis-nn" }, { "text": "Energy relaxation rate of 2D hole gas in GaAs/InGaAs/GaAs quantum well\n within wide range of conductivitiy: The nonohmic conductivity of 2D hole gas (2DHG) in single\n$GaAsIn_{0.2}Ga_{0.8}AsGaAs$ quantum well structures within the temperature\nrange of 1.4 - 4.2K, the carrier's densities $p=(1.5-8)\\cdot10^{15}m^{-2}$ and\na wide range of conductivities $(10^{-4}-100)G_0$ ($G_0=e^2/\\pi\\,h$) was\ninvestigated. It was shown that at conductivity $\\sigma>G_0$ the energy\nrelaxation rate $P(T_h,T_L)$ is well described by the conventional theory (P.J.\nPrice J. Appl. Phys. 53, 6863 (1982)), which takes into account scattering on\nacoustic phonons with both piezoelectric and deformational potential coupling\nto holes. At the conductivity range $0.01G_0<\\sigma\\alpha^*$ the\nentanglement entropy (EE) of excited eigenstates retains a logarithmic\ndivergence similar to the one observed for the ground state of the same model,\nwhile for $\\alpha<\\alpha^*$ EE displays an algebraic growth with the subsystem\nsize $l$, $S_l\\sim l^{\\beta}$, with $0<\\beta<1$. We find that $\\alpha^* \\approx\n1$ coincides with the delocalization transition $\\alpha_c$ in the middle of the\nmany-body spectrum. An interpretation of these results based on the structure\nof the RG rules is proposed, which is due to {\\it rainbow} proliferation for\nvery long-range interactions $\\alpha\\ll 1$. We also investigate the effective\ntemperature dependence of the EE allowing us to study the half-chain\nentanglement entropy of eigenstates at different energy densities, where we\nfind that the crossover in EE occurs at $\\alpha^* < 1$.", "category": "cond-mat_dis-nn" }, { "text": "Consistency capacity of reservoir computers: We study the propagation and distribution of information-carrying signals\ninjected in dynamical systems serving as a reservoir computers. A multivariate\ncorrelation analysis in tailored replica tests reveals consistency spectra and\ncapacities of a reservoir. These measures provide a high-dimensional portrait\nof the nonlinear functional dependence on the inputs. For multiple inputs a\nhierarchy of capacity measures characterizes the interference of signals from\neach source. For each input the time-resolved capacity forms a nonlinear fading\nmemory profile. We illustrate the methodology with various types of echo state\nnetworks.", "category": "cond-mat_dis-nn" }, { "text": "Fano Resonances in Flat Band Networks: Linear wave equations on Hamiltonian lattices with translational invariance\nare characterized by an eigenvalue band structure in reciprocal space. Flat\nband lattices have at least one of the bands completely dispersionless. Such\nbands are coined flat bands. Flat bands occur in fine-tuned networks, and can\nbe protected by (e.g. chiral) symmetries. Recently a number of such systems\nwere realized in structured optical systems, exciton-polariton condensates, and\nultracold atomic gases. Flat band networks support compact localized modes.\nLocal defects couple these compact modes to dispersive states and generate Fano\nresonances in the wave propagation. Disorder (i.e. a finite density of defects)\nleads to a dense set of Fano defects, and to novel scaling laws in the\nlocalization length of disordered dispersive states. Nonlinearities can\npreserve the compactness of flat band modes, along with renormalizing (tuning)\ntheir frequencies. These strictly compact nonlinear excitations induce tunable\nFano resonances in the wave propagation of a nonlinear flat band lattice.", "category": "cond-mat_dis-nn" }, { "text": "Identification of phases in scale-free networks: There is a pressing need for a description of complex systems that includes\nconsiderations of the underlying network of interactions, for a diverse range\nof biological, technological and other networks. In this work relationships\nbetween second-order phase transitions and the power laws associated with\nscale-free networks are directly quantified. A unique unbiased partitioning of\ncomplex networks (exemplified in this work by software architectures) into\nhigh- and low-connectivity regions can be made. Other applications to finance\nand aerogels are outlined.", "category": "cond-mat_dis-nn" }, { "text": "The spike-timing-dependent learning rule to encode spatiotemporal\n patterns in a network of spiking neurons: We study associative memory neural networks based on the Hodgkin-Huxley type\nof spiking neurons. We introduce the spike-timing-dependent learning rule, in\nwhich the time window with the negative part as well as the positive part is\nused to describe the biologically plausible synaptic plasticity. The learning\nrule is applied to encode a number of periodical spatiotemporal patterns, which\nare successfully reproduced in the periodical firing pattern of spiking neurons\nin the process of memory retrieval. The global inhibition is incorporated into\nthe model so as to induce the gamma oscillation. The occurrence of gamma\noscillation turns out to give appropriate spike timings for memory retrieval of\ndiscrete type of spatiotemporal pattern. The theoretical analysis to elucidate\nthe stationary properties of perfect retrieval state is conducted in the limit\nof an infinite number of neurons and shows the good agreement with the result\nof numerical simulations. The result of this analysis indicates that the\npresence of the negative and positive parts in the form of the time window\ncontributes to reduce the size of crosstalk term, implying that the time window\nwith the negative and positive parts is suitable to encode a number of\nspatiotemporal patterns. We draw some phase diagrams, in which we find various\ntypes of phase transitions with change of the intensity of global inhibition.", "category": "cond-mat_dis-nn" }, { "text": "On quantum and relativistic mechanical analogues in mean field spin\n models: Conceptual analogies among statistical mechanics and classical (or quantum)\nmechanics often appeared in the literature. For classical two-body mean field\nmodels, an analogy develops into a proper identification between the free\nenergy of Curie-Weiss type magnetic models and the Hamilton-Jacobi action for a\none dimensional mechanical system. Similarly, the partition function plays the\nrole of the wave function in quantum mechanics and satisfies the heat equation\nthat plays, in this context, the role of the Schrodinger equation in quantum\nmechanics. We show that this identification can be remarkably extended to\ninclude a wide family of magnetic models classified by normal forms of suitable\nreal algebraic dispersion curves. In all these cases, the model turns out to be\ncompletely solvable as the free energy as well as the order parameter are\nobtained as solutions of an integrable nonlinear PDE of Hamilton-Jacobi type.\nWe observe that the mechanical analog of these models can be viewed as the\nrelativistic analog of the Curie-Weiss model and this helps to clarify the\nconnection between generalised self-averaging and in statistical thermodynamics\nand the semi-classical dynamics of viscous conservation laws.", "category": "cond-mat_dis-nn" }, { "text": "Kinetic growth walks on complex networks: Kinetically grown self-avoiding walks on various types of generalized random\nnetworks have been studied. Networks with short- and long-tailed degree\ndistributions $P(k)$ were considered ($k$, degree or connectivity), including\nscale-free networks with $P(k) \\sim k^{-\\gamma}$. The long-range behaviour of\nself-avoiding walks on random networks is found to be determined by finite-size\neffects. The mean self-intersection length of non-reversal random walks, $$,\nscales as a power of the system size $N$: $ \\sim N^{\\beta}$, with an\nexponent $\\beta = 0.5$ for short-tailed degree distributions and $\\beta < 0.5$\nfor scale-free networks with $\\gamma < 3$. The mean attrition length of kinetic\ngrowth walks, $$, scales as $ \\sim N^{\\alpha}$, with an exponent\n$\\alpha$ which depends on the lowest degree in the network. Results of\napproximate probabilistic calculations are supported by those derived from\nsimulations of various kinds of networks. The efficiency of kinetic growth\nwalks to explore networks is largely reduced by inhomogeneity in the degree\ndistribution, as happens for scale-free networks.", "category": "cond-mat_dis-nn" }, { "text": "Fermionic many-body localization for random and quasiperiodic systems in\n the presence of short- and long-range interactions: We study many-body localization (MBL) for interacting one-dimensional lattice\nfermions in random (Anderson) and quasiperiodic (Aubry-Andre) models, focusing\non the role of interaction range. We obtain the MBL quantum phase diagrams by\ncalculating the experimentally relevant inverse participation ratio (IPR) at\nhalf-filling using exact diagonalization methods and extrapolating to the\ninfinite system size. For short-range interactions, our results produce in the\nphase diagram a qualitative symmetry between weak and strong interaction\nlimits. For long-range interactions, no such symmetry exists as the strongly\ninteracting system is always many-body localized, independent of the effective\ndisorder strength, and the system is analogous to a pinned Wigner crystal. We\nobtain various scaling exponents for the IPR, suggesting conditions for\ndifferent MBL regimes arising from interaction effects.", "category": "cond-mat_dis-nn" }, { "text": "An associative memory of Hodgkin-Huxley neuron networks with\n Willshaw-type synaptic couplings: An associative memory has been discussed of neural networks consisting of\nspiking N (=100) Hodgkin-Huxley (HH) neurons with time-delayed couplings, which\nmemorize P patterns in their synaptic weights. In addition to excitatory\nsynapses whose strengths are modified after the Willshaw-type learning rule\nwith the 0/1 code for quiescent/active states, the network includes uniform\ninhibitory synapses which are introduced to reduce cross-talk noises. Our\nsimulations of the HH neuron network for the noise-free state have shown to\nyield a fairly good performance with the storage capacity of $\\alpha_c = P_{\\rm\nmax}/N \\sim 0.4 - 2.4$ for the low neuron activity of $f \\sim 0.04-0.10$. This\nstorage capacity of our temporal-code network is comparable to that of the\nrate-code model with the Willshaw-type synapses. Our HH neuron network is\nrealized not to be vulnerable to the distribution of time delays in couplings.\nThe variability of interspace interval (ISI) of output spike trains in the\nprocess of retrieving stored patterns is also discussed.", "category": "cond-mat_dis-nn" }, { "text": "Valley Hall effect in disordered monolayer MoS2 from first principles: Electrons in certain two-dimensional crystals possess a pseudospin degree of\nfreedom associated with the existence of two inequivalent valleys in the\nBrillouin zone. If, as in monolayer MoS2, inversion symmetry is broken and\ntime-reversal symmetry is present, equal and opposite amounts of k-space Berry\ncurvature accumulate in each of the two valleys. This is conveniently\nquantified by the integral of the Berry curvature over a single valley - the\nvalley Hall conductivity. We generalize this definition to include\ncontributions from disorder described with the supercell approach, by mapping\n(\"unfolding\") the Berry curvature from the folded Brillouin zone of the\ndisordered supercell onto the normal Brillouin zone of the pristine crystal,\nand then averaging over several realizations of disorder. We use this scheme to\nstudy from first-principles the effect of sulfur vacancies on the valley Hall\nconductivity of monolayer MoS2. In dirty samples the intrinsic valley Hall\nconductivity receives gating-dependent corrections that are only weakly\ndependent on the impurity concentration, consistent with side-jump scattering\nand the unfolded Berry curvature can be interpreted as a k-space resolved\nside-jump. At low impurity concentrations skew scattering dominates, leading to\na divergent valley Hall conductivity in the clean limit. The implications for\nthe recently-observed photoinduced anomalous Hall effect are discussed.", "category": "cond-mat_dis-nn" }, { "text": "Numerical Study of a Many-Body Localized System Coupled to a Bath: We use exact diagonalization to study the breakdown of many-body localization\nin a strongly disordered and interacting system coupled to a thermalizing\nenvironment. We show that the many-body level statistics cross over from\nPoisson to GOE, and the localized eigenstates thermalize, with the crossover\ncoupling decreasing with the size of the bath in a manner consistent with the\nhypothesis that an infinitesimally small coupling to a thermodynamic bath\nshould destroy localization of the eigenstates. However, signatures of\nincomplete localization survive in spectral functions of local operators even\nwhen the coupling to the environment is non-zero. These include a discrete\nspectrum and a gap at zero frequency. Both features are washed out by line\nbroadening as one increases the coupling to the bath.", "category": "cond-mat_dis-nn" }, { "text": "Energy barriers in spin glasses: For an Ising spin glass on a hierarchical lattice, we show that the energy\nbarrier to be overcome during the flip of a domain of size L scales as L to the\npower d-1 for all dimensions d. We do this by investigating appropriate lower\nbounds to the barrier energy, which can be evaluated using an algorithm that\nremains fast for large system sizes and dimensions. The asymptotic limit of\ninfinite dimensions is evaluated analytically.", "category": "cond-mat_dis-nn" }, { "text": "Fractal fluctuations at mixed-order transitions in interdependent\n networks: We study the geometrical features of the order parameter's fluctuations near\nthe critical point of mixed-order phase transitions in randomly interdependent\nspatial networks. In contrast to continuous transitions, where the structure of\nthe order parameter at criticality is fractal, in mixed-order transitions the\nstructure of the order parameter is known to be compact. Remarkably, we find\nthat although being compact, the fluctuations of the order parameter close to\nmixed-order transitions are fractal up to a well-defined correlation length\n$\\xi'$, which diverges when approaching the critical threshold. We characterize\nthe self-similar nature of these critical fluctuations through their fractal\ndimension, $d_f'=3d/4$, and correlation length exponent, $\\nu'=2/d$, where $d$\nis the dimension of the system. By means of percolation and magnetization, we\ndemonstrate that $d_f'$ and $\\nu'$ are independent on the symmetry of the\nunderlying process for any $d$ of the underlying networks.", "category": "cond-mat_dis-nn" }, { "text": "The disordered-free-moment phase: a low-field disordered state in\n spin-gap antiferromagnets with site dilution: Site dilution of spin-gapped antiferromagnets leads to localized free\nmoments, which can order antiferromagnetically in two and higher dimensions.\nHere we show how a weak magnetic field drives this order-by-disorder state into\na novel disordered-free-moment phase, characterized by the formation of local\nsinglets between neighboring moments and by localized moments aligned\nantiparallel to the field. This disordered phase is characterized by the\nabsence of a gap, as it is the case in a Bose glass. The associated\nfield-driven quantum phase transition is consistent with the universality of a\nsuperfluid-to-Bose-glass transition. The robustness of the\ndisordered-free-moment phase and its prominent features, in particular a series\nof pseudo-plateaus in the magnetization curve, makes it accessible and relevant\nto experiments.", "category": "cond-mat_dis-nn" }, { "text": "Application of semidefinite programming to maximize the spectral gap\n produced by node removal: The smallest positive eigenvalue of the Laplacian of a network is called the\nspectral gap and characterizes various dynamics on networks. We propose\nmathematical programming methods to maximize the spectral gap of a given\nnetwork by removing a fixed number of nodes. We formulate relaxed versions of\nthe original problem using semidefinite programming and apply them to example\nnetworks.", "category": "cond-mat_dis-nn" }, { "text": "Kinetic Theory Approach to the SK Spin Glass Model with Glauber Dynamics: I present a new method to analyze Glauber dynamics of the\nSherrington-Kirkpatrick (SK) spin glass model. The method is based on ideas\nused in the classical kinetic theory of fluids. I apply it to study spin\ncorrelations in the high temperature phase ($T\\ge T_c$) of the SK model at zero\nexternal field. The zeroth order theory is equivalent to a disorder dependent\nlocal equilibrium approximation. Its predictions agree well with computer\nsimulation results. The first order theory involves coupled evolution equations\nfor the spin correlations and the dynamic (excess) parts of the local field\ndistributions. It accounts qualitatively for the error made in the zeroth\napproximation.", "category": "cond-mat_dis-nn" }, { "text": "Quantum simulation of long range $XY$ quantum spin glass with strong\n area-law violation using trapped ions: Ground states of local Hamiltonians are known to obey the entanglement\nentropy area law. While area law violation of a mild kind (logarithmic) is\ncommonly encountered, strong area-law violation (more than logarithmic) is\nrare. In this paper, we study the long range quantum spin glass in one\ndimension whose couplings are disordered and fall off with distance as a\npower-law. We show that this system exhibits more than logarithmic area law\nviolation in its ground state. Strikingly this feature is found to be true even\nin the short range regime in sharp contrast to the spinless long range\ndisordered fermionic model. This necessitates the study of large systems for\nthe quantum $XY$ spin glass model which is challenging since these numerical\nmethods depend on the validity of the area law. This situation lends itself\nnaturally for the exploration of a quantum simulation approach. We present a\nproof-of-principle implementation of this non-trivially interacting spin model\nusing trapped ions and provide a detailed study of experimentally realistic\nparameters.", "category": "cond-mat_dis-nn" }, { "text": "Slow dynamics and stress relaxation in a liquid as an elastic medium: We propose a new framework to discuss the transition from exponential\nrelaxation in a liquid to the regime of slow dynamics. For the purposes of\nstress relaxation, we show that a liquid can be treated as an elastic medium.\nWe discuss that, on lowering the temperature, the feed-forward interaction\nmechanism between local relaxation events becomes operative, and results in\nslow relaxation.", "category": "cond-mat_dis-nn" }, { "text": "Low-temperature kinetics of exciton-exciton annihilation of weakly\n localized one-dimensional Frenkel excitons: We present results of numerical simulations of the kinetics of\nexciton-exciton annihilation of weakly localized one-dimensional Frenkel\nexcitons at low temperatures. We find that the kinetics is represented by two\nwell-distinguished components: a fast short-time decay and a very slow\nlong-time tail. The former arises from excitons that initially reside in states\nbelonging to the same localization segment of the chain, while the slow\ncomponent is caused by excitons created on different localization segments. We\nshow that the usual bi-molecular theory fails in the description of the\nbehavior found. We also present a qualitative analytical explanation of the\nnon-exponential behavior observed in both the short- and the long-time decay\ncomponents.", "category": "cond-mat_dis-nn" }, { "text": "Degree Distribution of Competition-Induced Preferential Attachment\n Graphs: We introduce a family of one-dimensional geometric growth models, constructed\niteratively by locally optimizing the tradeoffs between two competing metrics,\nand show that this family is equivalent to a family of preferential attachment\nrandom graph models with upper cutoffs. This is the first explanation of how\npreferential attachment can arise from a more basic underlying mechanism of\nlocal competition. We rigorously determine the degree distribution for the\nfamily of random graph models, showing that it obeys a power law up to a finite\nthreshold and decays exponentially above this threshold.\n We also rigorously analyze a generalized version of our graph process, with\ntwo natural parameters, one corresponding to the cutoff and the other a\n``fertility'' parameter. We prove that the general model has a power-law degree\ndistribution up to a cutoff, and establish monotonicity of the power as a\nfunction of the two parameters. Limiting cases of the general model include the\nstandard preferential attachment model without cutoff and the uniform\nattachment model.", "category": "cond-mat_dis-nn" }, { "text": "A generation-based particle-hole density-matrix renormalization group\n study of interacting quantum dots: The particle-hole version of the density-matrix renormalization-group method\n(PH-DMRG) is utilized to calculate the ground-state energy of an interacting\ntwo-dimensional quantum dot. We show that a modification of the method, termed\ngeneration-based PH-DMRG, leads to significant improvement of the results, and\ndiscuss its feasibility for the treatment of large systems. As another\napplication we calculate the addition spectrum.", "category": "cond-mat_dis-nn" }, { "text": "Full replica symmetry breaking in generalized mean--field spin glasses\n with reflection symmetry: The analysis of the solution with full replica symmetry breaking in the\nvicinity of $T_c$ of a general spin glass model with reflection symmetry is\nperformed. The leading term in the order parameter function expansion is\nobtained. Parisi equation for the model is written.", "category": "cond-mat_dis-nn" }, { "text": "Instantaneous normal modes in liquids: a heterogeneous-elastic-medium\n approach: The concept of vibrational density of states in glasses has been mirrored in\nliquids by the instantaneous-normal-mode spectrum. While in glasses\ninstantaneous configurations correspond to minima of the potential-energy\nhypersurface and all eigenvalues of the associated Hessian matrix are therefore\npositive, in liquids this is no longer true, and modes corresponding to both\npositive and negative eigenvalues exist. The instantaneous-normal-mode spectrum\nhas been numerically investigated in the past, and it has been demonstrated to\nbring important information on the liquid dynamics. A systematic deeper\ntheoretical understanding is now needed. Heterogeneous-elasticity theory has\nproven to be successful in explaining many details of the low-frequency\nexcitations in glasses, ranging from the thoroughly studied boson peak, down to\nthe more elusive non-phononic excitations observed in numerical simulations at\nthe lowest frequencies. Here we present an extension of\nheterogeneous-elasticity theory to the liquid state, and show that the outcome\nof the theory agrees well to the results of extensive molecular-dynamics\nsimulations of a model liquid at different temperatures. We show that the\nspectral shape strongly depends on temperature, being symmetric at high\ntemperatures and becoming rather asymmetric at low temperatures, close to the\ndynamical critical temperature. Most importantly, we demonstrate that the\ntheory naturally reproduces a surprising phenomenon, a zero-energy spectral\nsingularity with a cusp-like character developing in the vibrational spectra\nupon cooling. This feature, known from a few previous numerical studies, has\nbeen generally overlooked in the past due to a misleading representation of the\ndata. We provide a thorough analysis of this issue, based on both very accurate\npredictions of our theory, and computational studies of model liquid systems\nwith extended size.", "category": "cond-mat_dis-nn" }, { "text": "Condensation phenomena with distinguishable particles: We study real-space condensation phenomena in a type of classical stochastic\nprocesses (site-particle system), such as zero-range processes and urn models.\nWe here study a stochastic process in the Ehrenfest class, i.e., particles in a\nsite are distinguishable. In terms of the statistical mechanical analogue, the\nEhrenfest class obeys the Maxwell-Boltzmann statistics. We analytically clarify\nconditions for condensation phenomena in disordered cases in the Ehrenfest\nclass. In addition, we discuss the preferential urn model as an example of the\ndisordered urn model. It becomes clear that the quenched disorder property\nplays an important role in the occurrence of the condensation phenomenon in the\npreferential urn model. It is revealed that the preferential urn model shows\nthree types of condensation depending on the disorder parameters.", "category": "cond-mat_dis-nn" }, { "text": "Symmetry breaking between statistically equivalent, independent channels\n in a few-channel chaotic scattering: We study the distribution function $P(\\omega)$ of the random variable $\\omega\n= \\tau_1/(\\tau_1 + ... + \\tau_N)$, where $\\tau_k$'s are the partial Wigner\ndelay times for chaotic scattering in a disordered system with $N$ independent,\nstatistically equivalent channels. In this case, $\\tau_k$'s are i.i.d. random\nvariables with a distribution $\\Psi(\\tau)$ characterized by a \"fat\" power-law\nintermediate tail $\\sim 1/\\tau^{1 + \\mu}$, truncated by an exponential (or a\nlog-normal) function of $\\tau$. For $N = 2$ and N=3, we observe a surprisingly\nrich behavior of $P(\\omega)$ revealing a breakdown of the symmetry between\nidentical independent channels. For N=2, numerical simulations of the quasi\none-dimensional Anderson model confirm our findings.", "category": "cond-mat_dis-nn" }, { "text": "Magnetic and Thermodynamic Properties of the Collective Paramagnet-Spin\n Liquid Pyrochlore Tb2Ti2O7: In a recent letter [Phys. Rev. Lett. {\\bf 82}, 1012 (1999)] it was found that\nthe Tb$^{3+}$ magnetic moments in the Tb$_2$Ti$_2$O$_7$ pyrochlore lattice of\ncorner-sharing tetrahedra remain in a {\\it collective paramagnetic} state down\nto 70mK. In this paper we present results from d.c. magnetic susceptibility,\nspecific heat data, inelastic neutron scattering measurements, and crystal\nfield calculations that strongly suggest that (1) the Tb$^{3+}$ ions in\nTb$_2$Ti$_2$O$_7$ possess a moment of approximatively 5$\\mu_{\\rm B}$, and (2)\nthe ground state $g-$tensor is extremely anisotropic below a temperature of\n$O(10^0)$K, with Ising-like Tb$^{3+}$ magnetic moments confined to point along\na local cubic $<111>$ diagonal (e.g. towards the middle of the tetrahedron).\nSuch a very large easy-axis Ising like anisotropy along a $<111>$ direction\ndramatically reduces the frustration otherwise present in a Heisenberg\npyrochlore antiferromagnet. The results presented herein underpin the\nconceptual difficulty in understanding the microscopic mechanism(s) responsible\nfor Tb$_2$Ti$_2$O$_7$ failing to develop long-range order at a temperature of\nthe order of the paramagnetic Curie-Weiss temperature $\\theta_{\\rm CW} \\approx\n-10^1$K. We suggest that dipolar interactions and extra perturbative exchange\ncoupling(s)beyond nearest-neighbors may be responsible for the lack of ordering\nof Tb$_2$Ti$_2$O$_7$.", "category": "cond-mat_dis-nn" }, { "text": "Response to a local quench of a system near many body localization\n transition: We consider a one dimensional spin $1/2$ chain with Heisenberg interaction in\na disordered parallel magnetic field. This system is known to exhibit the many\nbody localization (MBL) transition at critical strength of disorder. We analyze\nthe response of the chain when additional perpendicular magnetic field is\napplied to an individual spin and propose a method for accurate determination\nof the mobility edge via local spin measurements. We further demonstrate that\nthe exponential decrease of the spin response with the distance between\nperturbed spin and measured spin can be used to characterize the localization\nlength in the MBL phase.", "category": "cond-mat_dis-nn" }, { "text": "Approximate ground states of the random-field Potts model from graph\n cuts: While the ground-state problem for the random-field Ising model is\npolynomial, and can be solved using a number of well-known algorithms for\nmaximum flow or graph cut, the analogue random-field Potts model corresponds to\na multi-terminal flow problem that is known to be NP hard. Hence an efficient\nexact algorithm is very unlikely to exist. As we show here, it is nevertheless\npossible to use an embedding of binary degrees of freedom into the Potts spins\nin combination with graph-cut methods to solve the corresponding ground-state\nproblem approximately in polynomial time. We benchmark this heuristic algorithm\nusing a set of quasi-exact ground states found for small systems from long\nparallel tempering runs. For not too large number $q$ of Potts states, the\nmethod based on graph cuts finds the same solutions in a fraction of the time.\nWe employ the new technique to analyze the breakup length of the random-field\nPotts model in two dimensions.", "category": "cond-mat_dis-nn" }, { "text": "$T \\to 0$ mean-field population dynamics approach for the random\n 3-satisfiability problem: During the past decade, phase-transition phenomena in the random\n3-satisfiability (3-SAT) problem has been intensively studied by statistical\nphysics methods. In this work, we study the random 3-SAT problem by the\nmean-field first-step replica-symmetry-broken cavity theory at the limit of\ntemperature $T\\to 0$. The reweighting parameter $y$ of the cavity theory is\nallowed to approach infinity together with the inverse temperature $\\beta$ with\nfixed ratio $r=y / \\beta$. Focusing on the the system's space of satisfiable\nconfigurations, we carry out extensive population dynamics simulations using\nthe technique of importance sampling and we obtain the entropy density $s(r)$\nand complexity $\\Sigma(r)$ of zero-energy clusters at different $r$ values. We\ndemonstrate that the population dynamics may reach different fixed points with\ndifferent types of initial conditions. By knowing the trends of $s(r)$ and\n$\\Sigma(r)$ with $r$, we can judge whether a certain type of initial condition\nis appropriate at a given $r$ value. This work complements and confirms the\nresults of several other very recent theoretical studies.", "category": "cond-mat_dis-nn" }, { "text": "Self-Consistent Quantum-Field Theory for the Characterization of Complex\n Random Media by Short Laser Pulses: We present a quantum field theoretical method for the characterization of\ndisordered complex media with short laser pulses in an optical coherence\ntomography setup (OCT). We solve this scheme of coherent transport in space and\ntime with weighted essentially nonoscillatory methods (WENO). WENO is\npreferentially used for the determination of highly nonlinear and discontinuous\nprocesses including interference effects and phase transitions like Anderson\nlocalization of light. The theory determines spatiotemporal characteristics of\nthe scattering mean free path and the transmission cross section that are\ndirectly measurable in time-of-flight (ToF) and pump-probe experiments. The\nresults are a measure of the coherence of multiple scattering photons in\npassive as well as in optically soft random media. Our theoretical results of\nToF are instructive in spectral regions where material characteristics such as\nthe scattering mean free path and the diffusion coefficient are\nmethodologically almost insensitive to gain or absorption and to higher-order\nnonlinear effects. Our method is applicable to OCT and other advanced\nspectroscopy setups including samples of strongly scattering mono- and\npolydisperse complex nano- and microresonators.", "category": "cond-mat_dis-nn" }, { "text": "Effects of the network structural properties on its controllability: In a recent paper, it has been suggested that the controllability of a\ndiffusively coupled complex network, subject to localized feedback loops at\nsome of its vertices, can be assessed by means of a Master Stability Function\napproach, where the network controllability is defined in terms of the spectral\nproperties of an appropriate Laplacian matrix. Following that approach, a\ncomparison study is reported here among different network topologies in terms\nof their controllability. The effects of heterogeneity in the degree\ndistribution, as well as of degree correlation and community structure, are\ndiscussed.", "category": "cond-mat_dis-nn" }, { "text": "Basis Glass States: New Insights from the Potential Energy Landscape: Using the potential energy landscape formalism we show that, in the\ntemperature range in which the dynamics of a glass forming system is thermally\nactivated, there exists a unique set of \"basis glass states\" each of which is\nconfined to a single metabasin of the energy landscape of a glass forming\nsystem. These basis glass states tile the entire configuration space of the\nsystem, exhibit only secondary relaxation and are solid-like. Any macroscopic\nstate of the system (whether liquid or glass) can be represented as a\nsuperposition of basis glass states and can be described by a probability\ndistribution over these states. During cooling of a liquid from a high\ntemperature, the probability distribution freezes at sufficiently low\ntemperatures describing the process of liquid to glass transition. The time\nevolution of the probability distribution towards the equilibrium distribution\nduring subsequent aging describes the primary relaxation of a glass.", "category": "cond-mat_dis-nn" }, { "text": "Ground-state energy distribution of disordered many-body quantum systems: Extreme-value distributions are studied in the context of a broad range of\nproblems, from the equilibrium properties of low-temperature disordered systems\nto the occurrence of natural disasters. Our focus here is on the ground-state\nenergy distribution of disordered many-body quantum systems. We derive an\nanalytical expression that, upon tuning a parameter, reproduces with high\naccuracy the ground-state energy distribution of the systems that we consider.\nFor some models, it agrees with the Tracy-Widom distribution obtained from\nGaussian random matrices. They include transverse Ising models, the Sachdev-Ye\nmodel, and a randomized version of the PXP model. For other systems, such as\nBose-Hubbard models with random couplings and the disordered spin-1/2\nHeisenberg chain used to investigate many-body localization, the shapes are at\nodds with the Tracy-Widom distribution. Our analytical expression captures all\nof these distributions, thus playing a role to the lowest energy level similar\nto that played by the Brody distribution to the bulk of the spectrum.", "category": "cond-mat_dis-nn" }, { "text": "Metabolism of Social System: Random Boolean Network has been used to find out regulation patterns of genes\nin organism. his approach is very interesting to use in a game such as N Person\nPD. Here we assume that action is influenced by input in the form of choices of\ncooperate or defect he accepted from other agent or group of agents in the\nsystem. Number of cooperators, pay off value received by each agent, and\naverage value of the group pay off, are observed in every state, from initial\nstate chosen until it reaches its state cycle attractor. In simulation\nperformed here, we gain information that a system with large number agents\nbased on action on input K equals to two, will reach equilibrium and stable\ncondition over strategies taken out by its agents faster than higher input,\nthat is K equals to three. Equilibrium reached in longer interval, yet it is\nstable over strategies carried out by agents.", "category": "cond-mat_dis-nn" }, { "text": "The Quantum Spherical p-Spin-Glass Model: We study a quantum extension of the spherical $p$-spin-glass model using the\nimaginary-time replica formalism. We solve the model numerically and we discuss\ntwo analytical approximation schemes that capture most of the features of the\nsolution. The phase diagram and the physical properties of the system are\ndetermined in two ways: by imposing the usual conditions of thermodynamic\nequilibrium and by using the condition of marginal stability. In both cases,\nthe phase diagram consists of two qualitatively different regions. If the\ntransition temperature is higher than a critical value $T^{\\star}$, quantum\neffects are qualitatively irrelevant and the phase transition is {\\it second}\norder, as in the classical case. However, when quantum fluctuations depress the\ntransition temperature below $T^{\\star}$, the transition becomes {\\it first\norder}. The susceptibility is discontinuous and shows hysteresis across the\nfirst order line, a behavior reminiscent of that observed in the dipolar Ising\nspin-glass LiHo$_x$Y$_{1-x}$F$_4$ in an external transverse magnetic field. We\ndiscuss in detail the thermodynamics and the stationary dynamics of both\nstates. The spectrum of magnetic excitations of the equilibrium spin-glass\nstate is gaped, leading to an exponentially small specific heat at low\ntemperatures. That of the marginally stable state is gapless and its specific\nheat varies linearly with temperature, as generally observed in glasses at low\ntemperature. We show that the properties of the marginally stable state are\nclosely related to those obtained in studies of the real-time dynamics of the\nsystem weakly coupled to a quantum thermal bath. Finally, we discuss a possible\napplication of our results to the problem of polymers in random media.", "category": "cond-mat_dis-nn" }, { "text": "Adaptive Thouless--Anderson--Palmer equation for higher-order Markov\n random fields: The adaptive Thouless--Anderson--Palmer (TAP) mean-field approximation is one\nof the advanced mean-field approaches, and it is known as a powerful accurate\nmethod for Markov random fields (MRFs) with quadratic interactions (pairwise\nMRFs). In this study, an extension of the adaptive TAP approximation for MRFs\nwith many-body interactions (higher-order MRFs) is developed. We show that the\nadaptive TAP equation for pairwise MRFs is derived by naive mean-field\napproximation with diagonal consistency. Based on the equivalence of the\napproximate equation obtained from the naive mean-field approximation with\ndiagonal consistency and the adaptive TAP equation in pairwise MRFs, we\nformulate approximate equations for higher-order Boltzmann machines, which is\none of simplest higher-order MRFs, via the naive mean-field approximation with\ndiagonal consistency.", "category": "cond-mat_dis-nn" }, { "text": "Classical versus Quantum Structure of the Scattering Probability Matrix.\n Chaotic wave-guides: The purely classical counterpart of the Scattering Probability Matrix (SPM)\n$\\mid S_{n,m}\\mid^2$ of the quantum scattering matrix $S$ is defined for 2D\nquantum waveguides for an arbitrary number of propagating modes $M$. We compare\nthe quantum and classical structures of $\\mid S_{n,m}\\mid^2$ for a waveguide\nwith generic Hamiltonian chaos. It is shown that even for a moderate number of\nchannels, knowledge of the classical structure of the SPM allows us to predict\nthe global structure of the quantum one and, hence, understand important\nquantum transport properties of waveguides in terms of purely classical\ndynamics. It is also shown that the SPM, being an intensity measure, can give\nadditional dynamical information to that obtained by the Poincar\\`{e} maps.", "category": "cond-mat_dis-nn" }, { "text": "Quantum Statistical Physics of Glasses at Low Temperatures: We present a quantum statistical analysis of a microscopic mean-field model\nof structural glasses at low temperatures. The model can be thought of as\narising from a random Born von Karman expansion of the full interaction\npotential. The problem is reduced to a single-site theory formulated in terms\nof an imaginary-time path integral using replicas to deal with the disorder. We\nstudy the physical properties of the system in thermodynamic equilibrium and\ndevelop both perturbative and non-perturbative methods to solve the model. The\nperturbation theory is formulated as a loop expansion in terms of two-particle\nirreducible diagrams, and is carried to three-loop order in the effective\naction. The non-perturbative description is investigated in two ways, (i) using\na static approximation, and (ii) via Quantum Monte Carlo simulations. Results\nfor the Matsubara correlations at two-loop order perturbation theory are in\ngood agreement with those of the Quantum Monte Carlo simulations.\nCharacteristic low-temperature anomalies of the specific heat are reproduced,\nboth in the non-perturbative static approximation, and from a three-loop\nperturbative evaluation of the free energy. In the latter case the result so\nfar relies on using Matsubara correlations at two-loop order in the three-loop\nexpressions for the free energy, as self-consistent Matsubara correlations at\nthree-loop order are still unavailable. We propose to justify this by the good\nagreement of two-loop Matsubara correlations with those obtained\nnon-perturbatively via Quantum Monte Carlo simulations.", "category": "cond-mat_dis-nn" }, { "text": "Synchronization of phase oscillators on the hierarchical lattice: Synchronization of neurons forming a network with a hierarchical structure is\nessential for the brain to be able to function optimally. In this paper we\nstudy synchronization of phase oscillators on the most basic example of such a\nnetwork, namely, the hierarchical lattice. Each site of the lattice carries an\noscillator that is subject to noise. Pairs of oscillators interact with each\nother at a strength that depends on their hierarchical distance, modulated by a\nsequence of interaction parameters. We look at block averages of the\noscillators on successive hierarchical scales, which we think of as block\ncommunities. In the limit as the number of oscillators per community tends to\ninfinity, referred to as the hierarchical mean-field limit, we find a\nseparation of time scales, i.e., each block community behaves like a single\noscillator evolving on its own time scale. We argue that the evolution of the\nblock communities is given by a renormalized mean-field noisy Kuramoto\nequation, with a synchronization level that depends on the hierarchical scale\nof the block community. We find three universality classes for the\nsynchronization levels on successive hierarchical scales, characterized in\nterms of the sequence of interaction parameters.\n What makes our model specifically challenging is the non-linearity of the\ninteraction betweenthe oscillators. The main results of our paper therefore\ncome in three parts: (I) a conjecture about the nature of the renormalisation\ntransformation connecting successive hierarchical scales; (II) a truncation\napproximation that leads to a simplified renormalization transformation; (III)\na rigorous analysis of the simplified renormalization transformation. We\nprovide compelling arguments in support of (I) and (II), but a full\nverification remains an open problem.", "category": "cond-mat_dis-nn" }, { "text": "An Anomalously Elastic, Intermediate Phase in Randomly Layered\n Superfluids, Superconductors, and Planar Magnets: We show that layered quenched randomness in planar magnets leads to an\nunusual intermediate phase between the conventional ferromagnetic\nlow-temperature and paramagnetic high-temperature phases. In this intermediate\nphase, which is part of the Griffiths region, the spin-wave stiffness\nperpendicular to the random layers displays anomalous scaling behavior, with a\ncontinuously variable anomalous exponent, while the magnetization and the\nstiffness parallel to the layers both remain finite. Analogous results hold for\nsuperfluids and superconductors. We study the two phase transitions into the\nanomalous elastic phase, and we discuss the universality of these results, and\nimplications of finite sample size as well as possible experiments.", "category": "cond-mat_dis-nn" }, { "text": "Jamming in Hierarchical Networks: We study the Biroli-Mezard model for lattice glasses on a number of\nhierarchical networks. These networks combine certain lattice-like features\nwith a recursive structure that makes them suitable for exact renormalization\ngroup studies and provide an alternative to the mean-field approach. In our\nnumerical simulations here, we first explore their equilibrium properties with\nthe Wang-Landau algorithm. Then, we investigate their dynamical behavior using\na grand-canonical annealing algorithm. We find that the dynamics readily falls\nout of equilibrium and jams in many of our networks with certain constraints on\nthe neighborhood occupation imposed by the Biroli-Mezard model, even in cases\nwhere exact results indicate that no ideal glass transition exists. But while\nwe find that time-scales for the jams diverge, our simulations cannot ascertain\nsuch a divergence for a packing fraction distinctly above random close packing.\nIn cases where we allow hopping in our dynamical simulations, the jams on these\nnetworks generally disappear.", "category": "cond-mat_dis-nn" }, { "text": "How to calculate the fractal dimension of a complex network: the box\n covering algorithm: Covering a network with the minimum possible number of boxes can reveal\ninteresting features for the network structure, especially in terms of\nself-similar or fractal characteristics. Considerable attention has been\nrecently devoted to this problem, with the finding that many real networks are\nself-similar fractals. Here we present, compare and study in detail a number of\nalgorithms that we have used in previous papers towards this goal. We show that\nthis problem can be mapped to the well-known graph coloring problem and then we\nsimply can apply well-established algorithms. This seems to be the most\nefficient method, but we also present two other algorithms based on burning\nwhich provide a number of other benefits. We argue that the presented\nalgorithms provide a solution close to optimal and that another algorithm that\ncan significantly improve this result in an efficient way does not exist. We\noffer to anyone that finds such a method to cover his/her expenses for a 1-week\ntrip to our lab in New York (details in http://jamlab.org).", "category": "cond-mat_dis-nn" }, { "text": "Local fluctuation dissipation relation: In this letter I show that the recently proposed local version of the\nfluctuation dissipation relations follows from the general principle of\nstochastic stability in a way that is very similar to the usual proof of the\nfluctuation dissipation theorem for intensive quantities. Similar arguments can\nbe used to prove that all sites in an aging experiment stay at the same\neffective temperature at the same time.", "category": "cond-mat_dis-nn" }, { "text": "Quantum thermostatted disordered systems and sensitivity under\n compression: A one-dimensional quantum system with off diagonal disorder, consisting of a\nsample of conducting regions randomly interspersed within potential barriers is\nconsidered. Results mainly concerning the large $N$ limit are presented. In\nparticular, the effect of compression on the transmission coefficient is\ninvestigated. A numerical method to simulate such a system, for a physically\nrelevant number of barriers, is proposed. It is shown that the disordered model\nconverges to the periodic case as $N$ increases, with a rate of convergence\nwhich depends on the disorder degree. Compression always leads to a decrease of\nthe transmission coefficient which may be exploited to design\nnano-technological sensors. Effective choices for the physical parameters to\nimprove the sensitivity are provided. Eventually large fluctuations and rate\nfunctions are analysed.", "category": "cond-mat_dis-nn" }, { "text": "Denser glasses relax faster: a competition between rejuvenation and\n aging during in-situ high pressure compression at the atomic scale: A fascinating feature of metallic glasses is their ability to explore\ndifferent configurations under mechanical deformations. This effect is usually\nobserved through macroscopic observables, while little is known on the\nconsequence of the deformation at atomic level. Using the new generation of\nsynchrotrons, we probe the atomic motion and structure in a metallic glass\nunder hydrostatic compression, from the onset of the perturbation up to a\nseverely-compressed state. While the structure indicates reversible\ndensification under compression, the dynamic is dramatically accelerated and\nexhibits a hysteresis with two regimes. At low pressures, the atomic motion is\nheterogeneous with avalanche-like rearrangements suggesting rejuvenation, while\nunder further compression, aging leads to a super-diffusive dynamics triggered\nby internal stresses inherent to the glass. These results highlight the\ncomplexity of the atomic motion in non-ergodic systems and support a theory\nrecently developed to describe the surprising rejuvenation and strain hardening\nof metallic glasses under compression.", "category": "cond-mat_dis-nn" }, { "text": "Dynamical studies of the response function in a Spin Glass: Experiments on the time dependence of the response function of a Ag(11 at%Mn)\nspin glass at a temperature below the zero field spin glass temperature are\nused to explore the non-equilibrium nature of the spin glass phase. It is found\nthat the response function is only governed by the thermal history in the very\nneighbourhood of the actual measurement temperature. The thermal history\noutside this narrow region is irrelevant to the measured response. A result\nthat implies that the thermal history during cooling (cooling rate, wait times\netc.) is imprinted in the spin structure and is always retained when any higher\ntemperature is recovered. The observations are discussed in the light of a real\nspace droplet/domain phenomenology. The results also emphasise the importance\nof using controlled cooling procedures to acquire interpretable and\nreproducible experimental results on the non-equilibrium dynamics in spin\nglasses.", "category": "cond-mat_dis-nn" }, { "text": "Suppression of the virtual Anderson transition in a narrow impurity band\n of doped quantum well structures: Earlier we reported an observation at low temperatures of activation\nconductivity with small activation energies in strongly doped uncompensated\nlayers of p-GaAs/AlGaAs quantum wells. We attributed it to Anderson\ndelocalization of electronic states in the vicinity of the maximum of the\nnarrow impurity band. A possibility of such delocalization at relatively small\nimpurity concentration is related to the small width of the impurity band\ncharacterized by weak disorder. In this case the carriers were activated from\nthe \"bandtail\" while its presence was related to weak background compensation.\nHere we study an effect of the extrinsic compensation and of the impurity\nconcentration on this \"virtual\" Anderson transition. It was shown that an\nincrease of compensation initially does not affect the Anderson transition,\nhowever at strong compensations the transition is suppressed due to increase of\ndisorder. In its turn, an increase of the dopant concentration initially leads\nto a suppression of the transition due an increase of disorder, the latter\nresulting from a partial overlap of the Hubbard bands. However at larger\nconcentration the conductivity becomes to be metallic due to Mott transition.", "category": "cond-mat_dis-nn" }, { "text": "Duality, Quantum Skyrmions and the Stability of an SO(3) Two-Dimensional\n Quantum Spin-Glass: Quantum topological excitations (skyrmions) are analyzed from the point of\nview of their duality to spin excitations in the different phases of a\ndisordered two-dimensional, short-range interacting, SO(3) quantum magnetic\nsystem of Heisenberg type. The phase diagram displays all the phases, which are\nallowed by the duality relation. We study the large distance behavior of the\ntwo-point correlation function of quantum skyrmions in each of these phases\nand, out of this, extract information about the energy spectrum and\nnon-triviality of these excitations. The skyrmion correlators present a\npower-law decay in the spin-glass(SG)-phase, indicating that these quantum\ntopological excitations are gapless but nontrivial in this phase. The SG phase\nis dual to the AF phase, in the sense that topological and spin excitations are\nrespectively gapless in each of them. The Berezinskii-Kosterlitz-Thouless\nmechanism guarantees the survival of the SG phase at $T \\neq 0$, whereas the AF\nphase is washed out to T=0 by the quantum fluctuations. Our results suggest a\nnew, more symmetric way of characterizing a SG-phase: one for which both the\norder and disorder parameters vanish, namely $<\\sigma > = 0 $, $<\\mu > =0 $,\nwhere $\\sigma$ is the spin and $\\mu$ is the topological excitation operators.", "category": "cond-mat_dis-nn" }, { "text": "Destruction of first-order phase transition in a random-field Ising\n model: The phase transitions that occur in an infinite-range-interaction Ising\nferromagnet in the presence of a double-Gaussian random magnetic field are\nanalyzed. Such random fields are defined as a superposition of two Gaussian\ndistributions, presenting the same width $\\sigma$. Is is argued that this\ndistribution is more appropriate for a theoretical description of real systems\nthan its simpler particular cases, i.e., the bimodal ($\\sigma=0$) and the\nsingle Gaussian distributions. It is shown that a low-temperature first-order\nphase transition may be destructed for increasing values of $\\sigma$, similarly\nto what happens in the compound $Fe_{x}Mg_{1-x}Cl_{2}$, whose\nfinite-temperature first-order phase transition is presumably destructed by an\nincrease in the field randomness.", "category": "cond-mat_dis-nn" }, { "text": "The birth of geometry in exponential random graphs: Inspired by the prospect of having discretized spaces emerge from random\ngraphs, we construct a collection of simple and explicit exponential random\ngraph models that enjoy, in an appropriate parameter regime, a roughly constant\nvertex degree and form very large numbers of simple polygons (triangles or\nsquares). The models avoid the collapse phenomena that plague naive graph\nHamiltonians based on triangle or square counts. More than that, statistically\nsignificant numbers of other geometric primitives (small pieces of regular\nlattices, cubes) emerge in our ensemble, even though they are not in any way\nexplicitly pre-programmed into the formulation of the graph Hamiltonian, which\nonly depends on properties of paths of length 2. While much of our motivation\ncomes from hopes to construct a graph-based theory of random geometry\n(Euclidean quantum gravity), our presentation is completely self-contained\nwithin the context of exponential random graph theory, and the range of\npotential applications is considerably more broad.", "category": "cond-mat_dis-nn" }, { "text": "Percolation in Media with Columnar Disorder: We study a generalization of site percolation on a simple cubic lattice,\nwhere not only single sites are removed randomly, but also entire parallel\ncolumns of sites. We show that typical clusters near the percolation transition\nare very anisotropic, with different scaling exponents for the sizes parallel\nand perpendicular to the columns. Below the critical point there is a Griffiths\nphase where cluster size distributions and spanning probabilities in the\ndirection parallel to the columns have power law tails with continuously\nvarying non-universal powers. This region is very similar to the Griffiths\nphase in subcritical directed percolation with frozen disorder in the preferred\ndirection, and the proof follows essentially the same arguments as in that\ncase. But in contrast to directed percolation in disordered media, the number\nof active (\"growth\") sites in a growing cluster at criticality shows a power\nlaw, while the probability of a cluster to continue to grow shows logarithmic\nbehavior.", "category": "cond-mat_dis-nn" }, { "text": "Thermodynamic properties of extremely diluted symmetric Q-Ising neural\n networks: Using the replica-symmetric mean-field theory approach the thermodynamic and\nretrieval properties of extremely diluted {\\it symmetric} $Q$-Ising neural\nnetworks are studied. In particular, capacity-gain parameter and\ncapacity-temperature phase diagrams are derived for $Q=3, 4$ and $Q=\\infty$.\nThe zero-temperature results are compared with those obtained from a study of\nthe dynamics of the model. Furthermore, the de Almeida-Thouless line is\ndetermined. Where appropriate, the difference with other $Q$-Ising\narchitectures is outlined.", "category": "cond-mat_dis-nn" }, { "text": "Logarithmic Entanglement Lightcone in Many-Body Localized Systems: We theoretically study the response of a many-body localized system to a\nlocal quench from a quantum information perspective. We find that the local\nquench triggers entanglement growth throughout the whole system, giving rise to\na logarithmic lightcone. This saturates the modified Lieb-Robinson bound for\nquantum information propagation in many-body localized systems previously\nconjectured based on the existence of local integrals of motion. In addition,\nnear the localization-delocalization transition, we find that the final states\nafter the local quench exhibit volume-law entanglement. We also show that the\nlocal quench induces a deterministic orthogonality catastrophe for highly\nexcited eigenstates, where the typical wave-function overlap between the pre-\nand post-quench eigenstates decays {\\it exponentially} with the system size.", "category": "cond-mat_dis-nn" }, { "text": "Local level statistics for optical and transport properties of\n disordered systems at finite temperature: It is argued that the (traditional) global level statistics which determines\nlocalization and coherent transport properties of disordered systems at zero\ntemperature (e.g. the Anderson model) becomes inappropriate when it comes to\nincoherent transport. We define local level statistics which proves to be\nrelevant for finite temperature incoherent transport and optics of\none-dimensional systems (e.g. molecular aggregates, conjugated polymers, etc.).", "category": "cond-mat_dis-nn" }, { "text": "Microscopic picture of aging in SiO2: We investigate the aging dynamics of amorphous SiO2 via molecular dynamics\nsimulations of a quench from a high temperature T_i to a lower temperature T_f.\nWe obtain a microscopic picture of aging dynamics by analyzing single particle\ntrajectories, identifying jump events when a particle escapes the cage formed\nby its neighbors, and by determining how these jumps depend on the waiting time\nt_w, the time elapsed since the temperature quench to T_f. We find that the\nonly t_w-dependent microscopic quantity is the number of jumping particles per\nunit time, which decreases with age. Similar to previous studies for fragile\nglass formers, we show here for the strong glass former SiO2 that neither the\ndistribution of jump lengths nor the distribution of times spent in the cage\nare t_w-dependent. We conclude that the microscopic aging dynamics is\nsurprisingly similar for fragile and strong glass formers.", "category": "cond-mat_dis-nn" }, { "text": "$T \\to 0$ mean-field population dynamics approach for the random\n 3-satisfiability problem: During the past decade, phase-transition phenomena in the random\n3-satisfiability (3-SAT) problem has been intensively studied by statistical\nphysics methods. In this work, we study the random 3-SAT problem by the\nmean-field first-step replica-symmetry-broken cavity theory at the limit of\ntemperature $T\\to 0$. The reweighting parameter $y$ of the cavity theory is\nallowed to approach infinity together with the inverse temperature $\\beta$ with\nfixed ratio $r=y / \\beta$. Focusing on the the system's space of satisfiable\nconfigurations, we carry out extensive population dynamics simulations using\nthe technique of importance sampling and we obtain the entropy density $s(r)$\nand complexity $\\Sigma(r)$ of zero-energy clusters at different $r$ values. We\ndemonstrate that the population dynamics may reach different fixed points with\ndifferent types of initial conditions. By knowing the trends of $s(r)$ and\n$\\Sigma(r)$ with $r$, we can judge whether a certain type of initial condition\nis appropriate at a given $r$ value. This work complements and confirms the\nresults of several other very recent theoretical studies.", "category": "cond-mat_dis-nn" }, { "text": "Euclidean random matrix theory: low-frequency non-analyticities and\n Rayleigh scattering: By calculating all terms of the high-density expansion of the euclidean\nrandom matrix theory (up to second-order in the inverse density) for the\nvibrational spectrum of a topologically disordered system we show that the\nlow-frequency behavior of the self energy is given by $\\Sigma(k,z)\\propto\nk^2z^{d/2}$ and not $\\Sigma(k,z)\\propto k^2z^{(d-2)/2}$, as claimed previously.\nThis implies the presence of Rayleigh scattering and long-time tails of the\nvelocity autocorrelation function of the analogous diffusion problem of the\nform $Z(t)\\propto t^{(d+2)/2}$.", "category": "cond-mat_dis-nn" }, { "text": "From complex to simple : hierarchical free-energy landscape renormalized\n in deep neural networks: We develop a statistical mechanical approach based on the replica method to\nstudy the design space of deep and wide neural networks constrained to meet a\nlarge number of training data. Specifically, we analyze the configuration space\nof the synaptic weights and neurons in the hidden layers in a simple\nfeed-forward perceptron network for two scenarios: a setting with random\ninputs/outputs and a teacher-student setting. By increasing the strength of\nconstraints,~i.e. increasing the number of training data, successive 2nd order\nglass transition (random inputs/outputs) or 2nd order crystalline transition\n(teacher-student setting) take place layer-by-layer starting next to the\ninputs/outputs boundaries going deeper into the bulk with the thickness of the\nsolid phase growing logarithmically with the data size. This implies the\ntypical storage capacity of the network grows exponentially fast with the\ndepth. In a deep enough network, the central part remains in the liquid phase.\nWe argue that in systems of finite width N, the weak bias field can remain in\nthe center and plays the role of a symmetry-breaking field that connects the\nopposite sides of the system. The successive glass transitions bring about a\nhierarchical free-energy landscape with ultrametricity, which evolves in space:\nit is most complex close to the boundaries but becomes renormalized into\nprogressively simpler ones in deeper layers. These observations provide clues\nto understand why deep neural networks operate efficiently. Finally, we present\nsome numerical simulations of learning which reveal spatially heterogeneous\nglassy dynamics truncated by a finite width $N$ effect.", "category": "cond-mat_dis-nn" }, { "text": "Critical and resonance phenomena in neural networks: Brain rhythms contribute to every aspect of brain function. Here, we study\ncritical and resonance phenomena that precede the emergence of brain rhythms.\nUsing an analytical approach and simulations of a cortical circuit model of\nneural networks with stochastic neurons in the presence of noise, we show that\nspontaneous appearance of network oscillations occurs as a dynamical\n(non-equilibrium) phase transition at a critical point determined by the noise\nlevel, network structure, the balance between excitatory and inhibitory\nneurons, and other parameters. We find that the relaxation time of neural\nactivity to a steady state, response to periodic stimuli at the frequency of\nthe oscillations, amplitude of damped oscillations, and stochastic fluctuations\nof neural activity are dramatically increased when approaching the critical\npoint of the transition.", "category": "cond-mat_dis-nn" }, { "text": "Q-Ising neural network dynamics: a comparative review of various\n architectures: This contribution reviews the parallel dynamics of Q-Ising neural networks\nfor various architectures: extremely diluted asymmetric, layered feedforward,\nextremely diluted symmetric, and fully connected. Using a probabilistic\nsignal-to-noise ratio analysis, taking into account all feedback correlations,\nwhich are strongly dependent upon these architectures the evolution of the\ndistribution of the local field is found. This leads to a recursive scheme\ndetermining the complete time evolution of the order parameters of the network.\nArbitrary Q and mainly zero temperature are considered. For the asymmetrically\ndiluted and the layered feedforward network a closed-form solution is obtained\nwhile for the symmetrically diluted and fully connected architecture the\nfeedback correlations prevent such a closed-form solution. For these symmetric\nnetworks equilibrium fixed-point equations can be derived under certain\nconditions on the noise in the system. They are the same as those obtained in a\nthermodynamic replica-symmetric mean-field theory approach.", "category": "cond-mat_dis-nn" }, { "text": "Spin glasses in the limit of an infinite number of spin components: We consider the spin glass model in which the number of spin components, m,\nis infinite. In the formulation of the problem appropriate for numerical\ncalculations proposed by several authors, we show that the order parameter\ndefined by the long-distance limit of the correlation functions is actually\nzero and there is only \"quasi long range order\" below the transition\ntemperature. We also show that the spin glass transition temperature is zero in\nthree dimensions.", "category": "cond-mat_dis-nn" }, { "text": "Scaling of level statistics at the metal-insulator transition: Using the Anderson model for disordered systems the fluctuations in electron\nspectra near the metal--insulator transition were numerically calculated for\nlattices of sizes up to 28 x 28 x 28 sites. The results show a finite--size\nscaling of both the level spacing distribution and the variance of number of\nstates in a given energy interval, that allows to locate the critical point and\nto determine the critical exponent of the localization length.", "category": "cond-mat_dis-nn" }, { "text": "Fluctuation-Induced Forces in Disordered Landau-Ginzburg Model: We discuss fluctuation-induced forces in a system described by a continuous\nLandau-Ginzburg model with a quenched disorder field, defined in a\n$d$-dimensional slab geometry $\\mathbb R^{d-1}\\times[0,L]$. A series\nrepresentation for the quenched free energy in terms of the moments of the\npartition function is presented. In each moment an order parameter-like\nquantity can be defined, with a particular correlation length of the\nfluctuations. For some specific strength of the non-thermal control parameter,\nit appears a moment of the partition function where the fluctuations associated\nto the order parameter-like quantity becomes long-ranged. In this situation,\nthese fluctuations become sensitive to the boundaries. In the Gaussian\napproximation, using the spectral zeta-function method, we evaluate a\nfunctional determinant for each moment of the partition function. The analytic\nstructure of each spectral zeta-function depending on the dimension of the\nspace for the case of Dirichlet, Neumann Laplacian and also periodic boundary\nconditions is discussed in a unified way. Considering the moment of the\npartition function with the largest correlation length of the fluctuations, we\nevaluate the induced force between the boundaries, for Dirichlet boundary\nconditions. We prove that the sign of the fluctuation-induced force for this\ncase depend in a non-trivial way on the strength of the non-thermal control\nparameter.", "category": "cond-mat_dis-nn" }, { "text": "Coupling-Matrix Approach to the Chern Number Calculation in Disordered\n Systems: The Chern number is often used to distinguish between different topological\nphases of matter in two-dimensional electron systems. A fast and efficient\ncoupling-matrix method is designed to calculate the Chern number in finite\ncrystalline and disordered systems. To show its effectiveness, we apply the\napproach to the Haldane model and the lattice Hofstadter model, the quantized\nChern numbers being correctly obtained. The disorder-induced topological phase\ntransition is well reproduced, when the disorder strength is increased beyond\nthe critical value. We expect the method to be widely applicable to the study\nof topological quantum numbers.", "category": "cond-mat_dis-nn" }, { "text": "Quantum Hall transitions: An exact theory based on conformal restriction: We revisit the problem of the plateau transition in the integer quantum Hall\neffect. Here we develop an analytical approach for this transition, based on\nthe theory of conformal restriction. This is a mathematical theory that was\nrecently developed within the context of the Schramm-Loewner evolution which\ndescribes the stochastic geometry of fractal curves and other stochastic\ngeometrical fractal objects in 2D space. Observables elucidating the connection\nwith the plateau transition include the so-called point-contact conductances\n(PCCs) between points on the boundary of the sample, described within the\nlanguage of the Chalker-Coddington network model. We show that the\ndisorder-averaged PCCs are characterized by classical probabilities for certain\ngeometric objects in the plane (pictures), occurring with positive statistical\nweights, that satisfy the crucial restriction property with respect to changes\nin the shape of the sample with absorbing boundaries. Upon combining this\nrestriction property with the expected conformal invariance at the transition\npoint, we employ the mathematical theory of conformal restriction measures to\nrelate the disorder-averaged PCCs to correlation functions of primary operators\nin a conformal field theory (of central charge $c=0$). We show how this can be\nused to calculate these functions in a number of geometries with various\nboundary conditions. Since our results employ only the conformal restriction\nproperty, they are equally applicable to a number of other critical disordered\nelectronic systems in 2D. For most of these systems, we also predict exact\nvalues of critical exponents related to the spatial behavior of various\ndisorder-averaged PCCs.", "category": "cond-mat_dis-nn" }, { "text": "Thermodynamics of spin systems on small-world hypergraphs: We study the thermodynamic properties of spin systems on small-world\nhypergraphs, obtained by superimposing sparse Poisson random graphs with p-spin\ninteractions onto a one-dimensional Ising chain with nearest-neighbor\ninteractions. We use replica-symmetric transfer-matrix techniques to derive a\nset of fixed-point equations describing the relevant order parameters and free\nenergy, and solve them employing population dynamics. In the special case where\nthe number of connections per site is of the order of the system size we are\nable to solve the model analytically. In the more general case where the number\nof connections is finite we determine the static and dynamic\nferromagnetic-paramagnetic transitions using population dynamics. The results\nare tested against Monte-Carlo simulations.", "category": "cond-mat_dis-nn" }, { "text": "Excited-Eigenstate Entanglement Properties of XX Spin Chains with Random\n Long-Range Interactions: Quantum information theoretical measures are useful tools for characterizing\nquantum dynamical phases. However, employing them to study excited states of\nrandom spin systems is a challenging problem. Here, we report results for the\nentanglement entropy (EE) scaling of excited eigenstates of random XX\nantiferromagnetic spin chains with long-range (LR) interactions decaying as a\npower law with distance with exponent $\\alpha$. To this end, we extend the\nreal-space renormalization group technique for excited states (RSRG-X) to solve\nthis problem with LR interaction. For comparison, we perform numerical exact\ndiagonalization (ED) calculations. From the distribution of energy level\nspacings, as obtained by ED for up to $N\\sim 18$ spins, we find indications of\na delocalization transition at $\\alpha_c \\approx 1$ in the middle of the energy\nspectrum. With RSRG-X and ED, we show that for $\\alpha>\\alpha^*$ the\nentanglement entropy (EE) of excited eigenstates retains a logarithmic\ndivergence similar to the one observed for the ground state of the same model,\nwhile for $\\alpha<\\alpha^*$ EE displays an algebraic growth with the subsystem\nsize $l$, $S_l\\sim l^{\\beta}$, with $0<\\beta<1$. We find that $\\alpha^* \\approx\n1$ coincides with the delocalization transition $\\alpha_c$ in the middle of the\nmany-body spectrum. An interpretation of these results based on the structure\nof the RG rules is proposed, which is due to {\\it rainbow} proliferation for\nvery long-range interactions $\\alpha\\ll 1$. We also investigate the effective\ntemperature dependence of the EE allowing us to study the half-chain\nentanglement entropy of eigenstates at different energy densities, where we\nfind that the crossover in EE occurs at $\\alpha^* < 1$.", "category": "cond-mat_dis-nn" }, { "text": "Evidence for universal scaling in the spin-glass phase: We perform Monte Carlo simulations of Ising spin-glass models in three and\nfour dimensions, as well as of Migdal-Kadanoff spin glasses on a hierarchical\nlattice. Our results show strong evidence for universal scaling in the\nspin-glass phase in all three models. Not only does this allow for a clean way\nto compare results obtained from different coupling distributions, it also\nsuggests that a so far elusive renormalization group approach within the\nspin-glass phase may actually be feasible.", "category": "cond-mat_dis-nn" }, { "text": "Universality and Quantum Criticality in Quasiperiodic Spin Chains: Quasiperiodic systems are aperiodic but deterministic, so their critical\nbehavior differs from that of clean systems as well as disordered ones.\nQuasiperiodic criticality was previously understood only in the special limit\nwhere the couplings follow discrete quasiperiodic sequences. Here we consider\ngeneric quasiperiodic modulations; we find, remarkably, that for a wide class\nof spin chains, generic quasiperiodic modulations flow to discrete sequences\nunder a real-space renormalization group transformation. These discrete\nsequences are therefore fixed points of a \\emph{functional} renormalization\ngroup. This observation allows for an asymptotically exact treatment of the\ncritical points. We use this approach to analyze the quasiperiodic Heisenberg,\nIsing, and Potts spin chains, as well as a phenomenological model for the\nquasiperiodic many-body localization transition.", "category": "cond-mat_dis-nn" }, { "text": "The two-star model: exact solution in the sparse regime and condensation\n transition: The $2$-star model is the simplest exponential random graph model that\ndisplays complex behavior, such as degeneracy and phase transition. Despite its\nimportance, this model has been solved only in the regime of dense\nconnectivity. In this work we solve the model in the finite connectivity\nregime, far more prevalent in real world networks. We show that the model\nundergoes a condensation transition from a liquid to a condensate phase along\nthe critical line corresponding, in the ensemble parameters space, to the\nErd\\\"os-R\\'enyi graphs. In the fluid phase the model can produce graphs with a\nnarrow degree statistics, ranging from regular to Erd\\\"os-R\\'enyi graphs, while\nin the condensed phase, the \"excess\" degree heterogeneity condenses on a single\nsite with degree $\\sim\\sqrt{N}$. This shows the unsuitability of the two-star\nmodel, in its standard definition, to produce arbitrary finitely connected\ngraphs with degree heterogeneity higher than Erd\\\"os-R\\'enyi graphs and\nsuggests that non-pathological variants of this model may be attained by\nsoftening the global constraint on the two-stars, while keeping the number of\nlinks hardly constrained.", "category": "cond-mat_dis-nn" }, { "text": "Strong magnetoresistance of disordered graphene: We study theoretically magnetoresistance (MR) of graphene with different\ntypes of disorder. For short-range disorder, the key parameter determining\nmagnetotransport properties---a product of the cyclotron frequency and\nscattering time---depends in graphene not only on magnetic field $H$ but also\non the electron energy $\\varepsilon$. As a result, a strong, square-root in\n$H$, MR arises already within the Drude-Boltzmann approach. The MR is\nparticularly pronounced near the Dirac point. Furthermore, for the same reason,\n\"quantum\" (separated Landau levels) and \"classical\" (overlapping Landau levels)\nregimes may coexist in the same sample at fixed $H.$ We calculate the\nconductivity tensor within the self-consistent Born approximation for the case\nof relatively high temperature, when Shubnikov-de Haas oscillations are\nsuppressed by thermal averaging. We predict a square-root MR both at very low\nand at very high $H:$ $[\\varrho_{xx}(H)-\\varrho_{xx}(0)]/\\varrho_{xx}(0)\\approx\nC \\sqrt{H},$ where $C$ is a temperature-dependent factor, different in the low-\nand strong-field limits and containing both \"quantum\" and \"classical\"\ncontributions. We also find a nonmonotonic dependence of the Hall coefficient\nboth on magnetic field and on the electron concentration. In the case of\nscreened charged impurities, we predict a strong temperature-independent MR\nnear the Dirac point. Further, we discuss the competition between disorder- and\ncollision-dominated mechanisms of the MR. In particular, we find that the\nsquare-root MR is always established for graphene with charged impurities in a\ngeneric gated setup at low temperature.", "category": "cond-mat_dis-nn" }, { "text": "Crackling Noise and Avalanches: Scaling, Critical Phenomena, and the\n Renormalization Group: In the past two decades or so, we have learned how to understand crackling\nnoise in a wide variety of systems. We review here the basic ideas and methods\nwe use to understand crackling noise - critical phenomena, universality, the\nrenormalization group, power laws, and universal scaling functions. These\nmethods and tools were originally developed to understand continuous phase\ntransitions in thermal and disordered systems, and we also introduce these more\ntraditional applications as illustrations of the basic ideas and phenomena.", "category": "cond-mat_dis-nn" }, { "text": "Monte Carlo studies of quantum and classical annealing on a double-well: We present results for a variety of Monte Carlo annealing approaches, both\nclassical and quantum, benchmarked against one another for the textbook\noptimization exercise of a simple one-dimensional double-well. In classical\n(thermal) annealing, the dependence upon the move chosen in a Metropolis scheme\nis studied and correlated with the spectrum of the associated Markov transition\nmatrix. In quantum annealing, the Path-Integral Monte Carlo approach is found\nto yield non-trivial sampling difficulties associated with the tunneling\nbetween the two wells. The choice of fictitious quantum kinetic energy is also\naddressed. We find that a ``relativistic'' kinetic energy form, leading to a\nhigher probability of long real space jumps, can be considerably more effective\nthan the standard one.", "category": "cond-mat_dis-nn" }, { "text": "Anomalous Skin Effects in Disordered Systems with a Single non-Hermitian\n Impurity: We explore anomalous skin effects at non-Hermitian impurities by studying\ntheir interplay with potential disorder and by exactly solving a minimal\nlattice model. A striking feature of the solvable single-impurity model is that\nthe presence of anisotropic hopping terms can induce a scale-free accumulation\nof all eigenstates opposite to the bulk hopping direction, although the\nnonmonotonic behavior is fine tuned and further increasing such hopping weakens\nand eventually reverses the effect. The interplay with bulk potential disorder,\nhowever, qualitatively enriches this phenomenology leading to a robust\nnonmonotonic localization behavior as directional hopping strengths are tuned.\nNonmonotonicity persists even in the limit of an entirely Hermitian bulk with a\nsingle non-Hermitian impurity.", "category": "cond-mat_dis-nn" }, { "text": "Distribution of critical temperature at Anderson localization: Based on a local mean-field theory approach at Anderson localization, we find\na distribution function of critical temperature from that of disorder. An\nessential point of this local mean-field theory approach is that the\ninformation of the wave-function multifractality is introduced. The\ndistribution function of the Kondo temperature ($T_{K}$) shows a power-law tail\nin the limit of $T_{K} \\rightarrow 0$ regardless of the Kondo coupling\nconstant. We also find that the distribution function of the ferromagnetic\ntransition temperature ($T_{c}$) gives a power-law behavior in the limit of\n$T_{c} \\rightarrow 0$ when an interaction parameter for ferromagnetic\ninstability lies below a critical value. However, the $T_{c}$ distribution\nfunction stops the power-law increasing behavior in the $T_{c} \\rightarrow 0$\nlimit and vanishes beyond the critical interaction parameter inside the\nferromagnetic phase. These results imply that the typical Kondo temperature\ngiven by a geometric average always vanishes due to finite density of the\ndistribution function in the $T_{K} \\rightarrow 0$ limit while the typical\nferromagnetic transition temperature shows a phase transition at the critical\ninteraction parameter. We propose that the typical transition temperature\nserves a criterion for quantum Griffiths phenomena vs. smeared transitions:\nQuantum Griffiths phenomena occur above the typical value of the critical\ntemperature while smeared phase transitions result at low temperatures below\nthe typical transition temperature. We speculate that the ferromagnetic\ntransition at Anderson localization shows the evolution from quantum Griffiths\nphenomena to smeared transitions around the critical interaction parameter at\nlow temperatures.", "category": "cond-mat_dis-nn" }, { "text": "Neural network enhanced hybrid quantum many-body dynamical distributions: Computing dynamical distributions in quantum many-body systems represents one\nof the paradigmatic open problems in theoretical condensed matter physics.\nDespite the existence of different techniques both in real-time and frequency\nspace, computational limitations often dramatically constrain the physical\nregimes in which quantum many-body dynamics can be efficiently solved. Here we\nshow that the combination of machine learning methods and complementary\nmany-body tensor network techniques substantially decreases the computational\ncost of quantum many-body dynamics. We demonstrate that combining kernel\npolynomial techniques and real-time evolution, together with deep neural\nnetworks, allows to compute dynamical quantities faithfully. Focusing on\nmany-body dynamical distributions, we show that this hybrid neural-network\nmany-body algorithm, trained with single-particle data only, can efficiently\nextrapolate dynamics for many-body systems without prior knowledge.\nImportantly, this algorithm is shown to be substantially resilient to numerical\nnoise, a feature of major importance when using this algorithm together with\nnoisy many-body methods. Ultimately, our results provide a starting point\ntowards neural-network powered algorithms to support a variety of quantum\nmany-body dynamical methods, that could potentially solve computationally\nexpensive many-body systems in a more efficient manner.", "category": "cond-mat_dis-nn" }, { "text": "Microscopic theory of OMAR based on kinetic equations for quantum spin\n correlations: The correlation kinetic equation approach is developed that allows describing\nspin correlations in a material with hopping transport. The quantum nature of\nspin is taken into account. The approach is applied to the problem of the\nbipolaron mechanism of organic magnetoresistance (OMAR) in the limit of large\nHubbard energy and small applied electric field. The spin relaxation that is\nimportant to magnetoresistance is considered to be due to hyperfine interaction\nwith atomic nuclei. It is shown that the lineshape of magnetoresistance depends\non short-range transport properties. Different model systems with identical\nhyperfine interaction but different statistics of electron hops lead to\ndifferent lineshapes of magnetoresistance including the two empirical laws\n$H^2/(H^2 + H_0^2)$ and $H^2/(|H| + H_0)^2$ that are commonly used to fit\nexperimental results.", "category": "cond-mat_dis-nn" }, { "text": "Functional Renormalization for Disordered Systems, Basic Recipes and\n Gourmet Dishes: We give a pedagogical introduction into the functional renormalization group\ntreatment of disordered systems. After a review of its phenomenology, we show\nwhy in the context of disordered systems a functional renormalization group\ntreatment is necessary, contrary to pure systems, where renormalization of a\nsingle coupling constant is sufficient. This leads to a disorder distribution,\nwhich after a finite renormalization becomes non-analytic, thus overcoming the\npredictions of the seemingly exact dimensional reduction. We discuss, how the\nnon-analyticity can be measured in a simulation or experiment. We then\nconstruct a renormalizable field theory beyond leading order. We discuss an\nelastic manifold embedded in N dimensions, and give the exact solution for N to\ninfinity. This is compared to predictions of the Gaussian replica variational\nansatz, using replica symmetry breaking. We further consider random field\nmagnets, and supersymmetry. We finally discuss depinning, both isotropic and\nanisotropic, and universal scaling function.", "category": "cond-mat_dis-nn" }, { "text": "\"Burning and sticking\" model for a porous material: suppression of the\n topological phase transition due to the backbone reinforcement effect: We introduce and study the \"burning-and-sticking\" (BS) lattice model for the\nporous material that involves sticking of emerging finite clusters to the\nmainland. In contrast with other single-cluster models, it does not demonstrate\nany phase transition: the backbone exists at arbitrarily low concentrations.\nThe same is true for hybrid models, where the sticking events occur with\nprobability $q$: the backbone survives at arbitrarily low $q$. Disappearance of\nthe phase transition is attributed to the backbone reinforcement effect,\ngeneric for models with sticking. A relation between BS and the cluster-cluster\naggregation is briefly discussed.", "category": "cond-mat_dis-nn" }, { "text": "Random elastic networks : strong disorder renormalization approach: For arbitrary networks of random masses connected by random springs, we\ndefine a general strong disorder real-space renormalization (RG) approach that\ngeneralizes the procedures introduced previously by Hastings [Phys. Rev. Lett.\n90, 148702 (2003)] and by Amir, Oreg and Imry [Phys. Rev. Lett. 105, 070601\n(2010)] respectively. The principle is to eliminate iteratively the elementary\noscillating mode of highest frequency associated with either a mass or a spring\nconstant. To explain the accuracy of the strong disorder RG rules, we compare\nwith the Aoki RG rules that are exact at fixed frequency.", "category": "cond-mat_dis-nn" }, { "text": "Dynamics of disordered elastic systems: We review in these notes some dynamical properties of interfaces in random\nmedia submitted to an external force. We focuss in particular to the response\nto a very small force (so called creep motion) and discuss various theoretical\naspects of this problem. We consider in details in particular the case of a one\ndimensional interface (domain wall).", "category": "cond-mat_dis-nn" }, { "text": "A Theory for Spin Glass Phenomena in Interacting Nanoparticle Systems: Dilute magnetic nanoparticle systems exhibit slow dynamics [1] due to a broad\ndistribution of relaxation times that can be traced to a correspondingly broad\ndistribution of particle sizes [1]. However, at higher concentrations\ninterparticle interactions lead to a slow dynamics that is qualitatively\nindistinguishable from that dislayed by atomic spin glasses. A theory is\nderived below that accounts quantitatively for the spin-glass behaviour. The\ntheory predicts that if the interactions become too strong the spin glass\nbehaviour disappears. This conclusion is in agreement with preliminary\nexperimental results.", "category": "cond-mat_dis-nn" }, { "text": "Fluctuations of random matrix products and 1D Dirac equation with random\n mass: We study the fluctuations of certain random matrix products $\\Pi_N=M_N\\cdots\nM_2M_1$ of $\\mathrm{SL}(2,\\mathbb{R})$, describing localisation properties of\nthe one-dimensional Dirac equation with random mass. In the continuum limit,\ni.e. when matrices $M_n$'s are close to the identity matrix, we obtain\nconvenient integral representations for the variance\n$\\Gamma_2=\\lim_{N\\to\\infty}\\mathrm{Var}(\\ln||\\Pi_N||)/N$. The case studied\nexhibits a saturation of the variance at low energy $\\varepsilon$ along with a\nvanishing Lyapunov exponent $\\Gamma_1=\\lim_{N\\to\\infty}\\ln||\\Pi_N||/N$, leading\nto the behaviour $\\Gamma_2/\\Gamma_1\\sim\\ln(1/|\\varepsilon|)\\to\\infty$ as\n$\\varepsilon\\to0$. Our continuum description sheds new light on the\nKappus-Wegner (band center) anomaly.", "category": "cond-mat_dis-nn" }, { "text": "Strong Disorder RG approach - a short review of recent developments: The Strong Disorder RG approach for random systems has been extended in many\nnew directions since our previous review of 2005 [Phys. Rep. 412, 277]. The aim\nof the present colloquium paper is thus to give an overview of these various\nrecent developments. In the field of quantum disordered models, recent progress\nconcern Infinite Disorder Fixed Points for short-ranged models in higher\ndimensions $d>1$, Strong Disorder Fixed Points for long-ranged models, scaling\nof the entanglement entropy in critical ground-states and after quantum\nquenches, the RSRG-X procedure to construct the whole set excited stated and\nthe RSRG-t procedure for the unitary dynamics in Many-Body-Localized Phases,\nthe Floquet dynamics of periodically driven chains, the dissipative effects\ninduced by the coupling to external baths, and Anderson Localization models. In\nthe field of classical disordered models, new applications include the contact\nprocess for epidemic spreading, the strong disorder renormalization procedure\nfor general master equations, the localization properties of random elastic\nnetworks and the synchronization of interacting non-linear dissipative\noscillators.", "category": "cond-mat_dis-nn" }, { "text": "Algorithms for 3D rigidity analysis and a first order percolation\n transition: A fast computer algorithm, the pebble game, has been used successfully to\nstudy rigidity percolation on 2D elastic networks, as well as on a special\nclass of 3D networks, the bond-bending networks. Application of the pebble game\napproach to general 3D networks has been hindered by the fact that the\nunderlying mathematical theory is, strictly speaking, invalid in this case. We\nconstruct an approximate pebble game algorithm for general 3D networks, as well\nas a slower but exact algorithm, the relaxation algorithm, that we use for\ntesting the new pebble game. Based on the results of these tests and additional\nconsiderations, we argue that in the particular case of randomly diluted\ncentral-force networks on BCC and FCC lattices, the pebble game is essentially\nexact. Using the pebble game, we observe an extremely sharp jump in the largest\nrigid cluster size in bond-diluted central-force networks in 3D, with the\npercolating cluster appearing and taking up most of the network after a single\nbond addition. This strongly suggests a first order rigidity percolation\ntransition, which is in contrast to the second order transitions found\npreviously for the 2D central-force and 3D bond-bending networks. While a first\norder rigidity transition has been observed for Bethe lattices and networks\nwith ``chemical order'', this is the first time it has been seen for a regular\nrandomly diluted network. In the case of site dilution, the transition is also\nfirst order for BCC, but results for FCC suggest a second order transition.\nEven in bond-diluted lattices, while the transition appears massively first\norder in the order parameter (the percolating cluster size), it is continuous\nin the elastic moduli. This, and the apparent non-universality, make this phase\ntransition highly unusual.", "category": "cond-mat_dis-nn" }, { "text": "Constructing local integrals of motion in the many-body localized phase: Many-body localization provides a generic mechanism of ergodicity breaking in\nquantum systems. In contrast to conventional ergodic systems, many-body\nlocalized (MBL) systems are characterized by extensively many local integrals\nof motion (LIOM), which underlie the absence of transport and thermalization in\nthese systems. Here we report a physically motivated construction of local\nintegrals of motion in the MBL phase. We show that any local operator (e.g., a\nlocal particle number or a spin flip operator), evolved with the system's\nHamiltonian and averaged over time, becomes a LIOM in the MBL phase. Such\noperators have a clear physical meaning, describing the response of the MBL\nsystem to a local perturbation. In particular, when a local operator represents\na density of some globally conserved quantity, the corresponding LIOM describes\nhow this conserved quantity propagates through the MBL phase. Being uniquely\ndefined and experimentally measurable, these LIOMs provide a natural tool for\ncharacterizing the properties of the MBL phase, both in experiments and\nnumerical simulations. We demonstrate the latter by numerically constructing an\nextensive set of LIOMs in the MBL phase of a disordered spin chain model. We\nshow that the resulting LIOMs are quasi-local, and use their decay to extract\nthe localization length and establish the location of the transition between\nthe MBL and ergodic phases.", "category": "cond-mat_dis-nn" }, { "text": "Viscosity and relaxation processes of the liquid become amorphous\n Al-Ni-REM alloys: The temperature and time dependencies of viscosity of the liquid alloys,\nAl87Ni8Y5, Al86Ni8La6, Al86Ni8Ce6, and the binary Al-Ni and Al-Y melts with Al\nconcentration over 90 at.% have been studied. Non-monotonic relaxation\nprocesses caused by destruction of nonequilibrium state inherited from the\nbasic-heterogeneous alloy have been found to take place in Al-Y, Al-Ni-REM\nmelts after the phase solid-liquid transition. The mechanism of nonmonotonic\nrelaxation in non-equilibrium melts has been suggested.", "category": "cond-mat_dis-nn" }, { "text": "Electric field control of magnetic properties and magneto-transport in\n composite multiferroics: We study magnetic state and electron transport properties of composite\nmultiferroic system consisting of a granular ferromagnetic thin film placed\nabove the ferroelectric substrate. Ferroelectricity and magnetism in this case\nare coupled by the long-range Coulomb interaction. We show that magnetic state\nand magneto-transport strongly depend on temperature, external electric field,\nand electric polarization of the substrate. Ferromagnetic order exists at\nfinite temperature range around ferroelectric Curie point. Outside the region\nthe film is in the superparamagnetic state. We demonstrate that magnetic phase\ntransition can be driven by an electric field and magneto-resistance effect has\ntwo maxima associated with two magnetic phase transitions appearing in the\nvicinity of the ferroelectric phase transition. We show that positions of these\nmaxima can be shifted by the external electric field and that the magnitude of\nthe magneto-resistance effect depends on the mutual orientation of external\nelectric field and polarization of the substrate.", "category": "cond-mat_dis-nn" }, { "text": "Near-field EM wave scattering from random self-affine fractal metal\n surfaces: spectral dependence of local field enhancements and their\n statistics in connection with SERS: By means of rigorous numerical simulation calculations based on the Green's\ntheorem integral equation formulation, we study the near EM field in the\nvicinity of very rough, one-dimensional self-affine fractal surfaces of Ag, Au,\nand Cu (for both vacuum and water propagating media) illuminated by a p\npolarized field. Strongly localized enhanced optical excitations (hot spots)\nare found, with electric field intensity enhancements of close to 4 orders of\nmagnitude the incident one, and widths below a tenth of the incoming\nwavelength. These effects are produced by roughness-induced surface-plasmon\npolariton excitation. We study the characteristics of these optical excitations\nas well as other properties of the surface electromagnetic field, such as its\nstatistics (probability density function, average and fluctuations), and their\ndependence on the excitation spectrum (in the visible and near infrared). Our\nstudy is relevant to the use of such self-affine fractals as surface-enhanced\nRaman scattering substrates, where large local and average field enhancements\nare desired.", "category": "cond-mat_dis-nn" }, { "text": "Magnitoelastic interaction and long-range magnetic ordering in\n two-dimesional ferromagnetics: The influence of magnitoelastic (ME) interaction on the stabilization of\nlong-range magnetic order (LMO) in the two-dimensional easy-plane ferromagnetic\nis investigated in this work. The account of ME exchange results in the root\ndispersion law of magnons and appearance of ME gap in the spectra of elementary\nexcitations. Such a behavior of the spectra testifies to the stabilization of\nLMO and finite Curie's temperature.", "category": "cond-mat_dis-nn" }, { "text": "Momentum Signatures of Site Percolation in Disordered 2D Ferromagnets: In this work, we consider a two-dimensional square lattice of pinned magnetic\nspins with nearest-neighbour interactions and we randomly replace a fixed\nproportion of spins with nonmagnetic defects carrying no spin. We focus on the\nlinear spin-wave regime and address the propagation of a spin-wave excitation\nwith initial momentum $k_0$. We compute the disorder-averaged momentum\ndistribution obtained at time $t$ and show that the system exhibits two\nregimes. At low defect density, typical disorder configurations only involve a\nsingle percolating magnetic cluster interspersed with single defects\nessentially and the physics is driven by Anderson localization. In this case,\nthe momentum distribution features the emergence of two known emblematic\nsignatures of coherent transport, namely the coherent backscattering (CBS) peak\nlocated at $-k_0$ and the coherent forward scattering (CFS) peak located at\n$k_0$. At long times, the momentum distribution becomes stationary. However,\nwhen increasing the defect density, site percolation starts to set in and\ntypical disorder configurations display more and more disconnected clusters of\ndifferent sizes and shapes. At the same time, the CFS peak starts to oscillate\nin time with well defined frequencies. These oscillation frequencies represent\neigenenergy differences in the regular, disorder-immune, part of the\nHamiltonian spectrum. This regular spectrum originates from the small-size\nmagnetic clusters and its weight grows as the system undergoes site percolation\nand small clusters proliferate. Our system offers a unique spectroscopic\nsignature of cluster formation in site percolation problems.", "category": "cond-mat_dis-nn" }, { "text": "Bond-disordered spin systems: Theory and application to doped high-Tc\n compounds: We examine the stability of magnetic order in a classical Heisenberg model\nwith quenched random exchange couplings. This system represents the spin\ndegrees of freedom in high-$T_\\textrm{c}$ compounds with immobile dopants.\nStarting from a replica representation of the nonlinear $\\sigma$-model, we\nperform a renormalization-group analysis. The importance of cumulants of the\ndisorder distribution to arbitrarily high orders necessitates a functional\nrenormalization scheme. From the renormalization flow equations we determine\nthe magnetic correlation length numerically as a function of the impurity\nconcentration and of temperature. From our analysis follows that\ntwo-dimensional layers can be magnetically ordered for arbitrarily strong but\nsufficiently diluted defects. We further consider the dimensional crossover in\na stack of weakly coupled layers. The resulting phase diagram is compared with\nexperimental data for La$_{2-x}$Sr$_x$CuO$_4$.", "category": "cond-mat_dis-nn" }, { "text": "Photonic structures with disorder immunity: Periodic and disordered media are known to possess different transport\nproperties, either classically or quantum-mechanically. This has been exhibited\nby effects such as Anderson localization in systems with disorder and the\nexistence of photonic bandgaps in the periodic case. In this paper we analyze\nthe transport properties of disordered waveguides with corners at very low\nfrequencies, finding that the spectrum, conductance and wavefunctions are\nimmune to disorder. Our waveguides are constructed by means of randomly\noriented straight segments and connected by corners at right angles. Taking\nadvantage of a trapping effect that manifests in the corner of a bent\nwaveguide, we can show that a tight-binding approximation describes the system\nreasonably well for any degree of disorder. This provides a wide set of\nnon-periodic geometries that preserve all the interesting transport properties\nof periodic media.", "category": "cond-mat_dis-nn" }, { "text": "Absence of Conventional Spin-Glass Transition in the Ising Dipolar\n System LiHo_xY_{1-x}F_4: The magnetic properties of single crystals of LiHo_xY_{1-x}F_4 with x=16.5%\nand x=4.5% were recorded down to 35 mK using a micro-SQUID magnetometer. While\nthis system is considered as the archetypal quantum spin glass, the detailed\nanalysis of our magnetization data indicates the absence of a phase transition,\nnot only in a transverse applied magnetic field, but also without field. A\nzero-Kelvin phase transition is also unlikely, as the magnetization seems to\nfollow a non-critical exponential dependence on the temperature. Our analysis\nthus unmasks the true, short-ranged nature of the magnetic properties of the\nLiHo_xY_{1-x}F_4 system, validating recent theoretical investigations\nsuggesting the lack of phase transition in this system.", "category": "cond-mat_dis-nn" }, { "text": "Distribution of the reflection eigenvalues of a weakly absorbing chaotic\n cavity: The scattering-matrix product SS+ of a weakly absorbing medium is related by\na unitary transformation to the time-delay matrix without absorption. It\nfollows from this relationship that the eigenvalues of SS+ for a weakly\nabsorbing chaotic cavity are distributed according to a generalized Laguerre\nensemble.", "category": "cond-mat_dis-nn" }, { "text": "Dynamics of strongly interacting systems: From Fock-space fragmentation\n to Many-Body Localization: We study the $t{-}V$ disordered spinless fermionic chain in the strong\ncoupling regime, $t/V\\rightarrow 0$. Strong interactions highly hinder the\ndynamics of the model, fragmenting its Hilbert space into exponentially many\nblocks in system size. Macroscopically, these blocks can be characterized by\nthe number of new degrees of freedom, which we refer to as movers. We focus on\ntwo limiting cases: Blocks with only one mover and the ones with a finite\ndensity of movers. The former many-particle block can be exactly mapped to a\nsingle-particle Anderson model with correlated disorder in one dimension. As a\nresult, these eigenstates are always localized for any finite amount of\ndisorder. The blocks with a finite density of movers, on the other side, show\nan MBL transition that is tuned by the disorder strength. Moreover, we provide\nnumerical evidence that its ergodic phase is diffusive at weak disorder.\nApproaching the MBL transition, we observe sub-diffusive dynamics at finite\ntime scales and find indications that this might be only a transient behavior\nbefore crossing over to diffusion.", "category": "cond-mat_dis-nn" }, { "text": "Hidden Quasicrystal in Hofstadter Butterfly: Topological description of hierarchical sets of spectral gaps of Hofstadter\nbutterfly is found to be encoded in a quasicrystal where magnetic flux plays\nthe role of a phase factor that shifts the origin of the quasiperiodic order.\nRevealing an intrinsic frustration at smallest energy scale, described by\n$\\zeta=2-\\sqrt{3}$, this irrational number characterizes the universal\nbutterfly and is related to two quantum numbers that includes the Chern number\nof quantum Hall states. With a periodic drive that induces phase transitions in\nthe system, the fine structure of the butterfly is shown to be amplified making\nstates with large topological invariants accessible experimentally .", "category": "cond-mat_dis-nn" }, { "text": "Thermodynamics of spin systems on small-world hypergraphs: We study the thermodynamic properties of spin systems on small-world\nhypergraphs, obtained by superimposing sparse Poisson random graphs with p-spin\ninteractions onto a one-dimensional Ising chain with nearest-neighbor\ninteractions. We use replica-symmetric transfer-matrix techniques to derive a\nset of fixed-point equations describing the relevant order parameters and free\nenergy, and solve them employing population dynamics. In the special case where\nthe number of connections per site is of the order of the system size we are\nable to solve the model analytically. In the more general case where the number\nof connections is finite we determine the static and dynamic\nferromagnetic-paramagnetic transitions using population dynamics. The results\nare tested against Monte-Carlo simulations.", "category": "cond-mat_dis-nn" }, { "text": "Weighted evolving networks: coupling topology and weights dynamics: We propose a model for the growth of weighted networks that couples the\nestablishment of new edges and vertices and the weights' dynamical evolution.\nThe model is based on a simple weight-driven dynamics and generates networks\nexhibiting the statistical properties observed in several real-world systems.\nIn particular, the model yields a non-trivial time evolution of vertices'\nproperties and scale-free behavior for the weight, strength and degree\ndistributions.", "category": "cond-mat_dis-nn" }, { "text": "Thermodynamic signature of growing amorphous order in glass-forming\n liquids: Although several theories relate the steep slowdown of glass formers to\nincreasing spatial correlations of some sort, standard static correlation\nfunctions show no evidence for this. We present results that reveal for the\nfirst time a qualitative thermodynamic difference between the high temperature\nand deeply supercooled equilibrium glass-forming liquid: the influence of\nboundary conditions propagates into the bulk over larger and larger\nlengthscales upon cooling, and, as this static correlation length grows, the\ninfluence decays nonexponentially. Increasingly long-range susceptibility to\nboundary conditions is expected within the random firt-order theory (RFOT) of\nthe glass transition, but a quantitative account of our numerical results\nrequires a generalization of RFOT where the surface tension between states\nfluctuates.", "category": "cond-mat_dis-nn" }, { "text": "\"Single Ring Theorem\" and the Disk-Annulus Phase Transition: Recently, an analytic method was developed to study in the large $N$ limit\nnon-hermitean random matrices that are drawn from a large class of circularly\nsymmetric non-Gaussian probability distributions, thus extending the existing\nGaussian non-hermitean literature. One obtains an explicit algebraic equation\nfor the integrated density of eigenvalues from which the Green's function and\naveraged density of eigenvalues could be calculated in a simple manner. Thus,\nthat formalism may be thought of as the non-hermitean analog of the method due\nto Br\\'ezin, Itzykson, Parisi and Zuber for analyzing hermitean non-Gaussian\nrandom matrices. A somewhat surprising result is the so called \"Single Ring\"\ntheorem, namely, that the domain of the eigenvalue distribution in the complex\nplane is either a disk or an annulus. In this paper we extend previous results\nand provide simple new explicit expressions for the radii of the eigenvalue\ndistiobution and for the value of the eigenvalue density at the edges of the\neigenvalue distribution of the non-hermitean matrix in terms of moments of the\neigenvalue distribution of the associated hermitean matrix. We then present\nseveral numerical verifications of the previously obtained analytic results for\nthe quartic ensemble and its phase transition from a disk shaped eigenvalue\ndistribution to an annular distribution. Finally, we demonstrate numerically\nthe \"Single Ring\" theorem for the sextic potential, namely, the potential of\nlowest degree for which the \"Single Ring\" theorem has non-trivial consequences.", "category": "cond-mat_dis-nn" }, { "text": "Spin-glass behavior in the random-anisotropy Heisenberg model: We perform Monte Carlo simulations in a random anisotropy magnet at a\nintermediate exchange to anisotropy ratio. We focus on the out of equilibrium\nrelaxation after a sudden quenching in the low temperature phase, well below\nthe freezing one. By analyzing both the aging dynamics and the violation of the\nFluctuation Dissipation relation we found strong evidence of a spin--glass like\nbehavior. In fact, our results are qualitatively similar to those\nexperimentally obtained recently in a Heisenberg-like real spin glass.", "category": "cond-mat_dis-nn" }, { "text": "Quantum dynamics in canonical and micro-canonical ensembles. Part I.\n Anderson localization of electrons: The new numerical approach for consideration of quantum dynamics and\ncalculations of the average values of quantum operators and time correlation\nfunctions in the Wigner representation of quantum statistical mechanics has\nbeen developed. The time correlation functions have been presented in the form\nof the integral of the Weyl's symbol of considered operators and the Fourier\ntransform of the product of matrix elements of the dynamic propagators. For the\nlast function the integral Wigner- Liouville's type equation has been derived.\nThe numerical procedure for solving this equation combining both molecular\ndynamics and Monte Carlo methods has been developed. For electrons in\ndisordered systems of scatterers the numerical results have been obtained for\nseries of the average values of the quantum operators including position and\nmomentum dispersions, average energy, energy distribution function as well as\nfor the frequency dependencies of tensor of electron conductivity and\npermittivity according to quantum Kubo formula. Zero or very small value of\nstatic conductivity have been considered as the manifestation of Anderson\nlocalization of electrons in 1D case. Independent evidence of Anderson\nlocalization comes from the behaviour of the calculated time dependence of\nposition dispersion.", "category": "cond-mat_dis-nn" }, { "text": "On Renyi entropies characterizing the shape and the extension of the\n phase space representation of quantum wave functions in disordered systems: We discuss some properties of the generalized entropies, called Renyi\nentropies and their application to the case of continuous distributions. In\nparticular it is shown that these measures of complexity can be divergent,\nhowever, their differences are free from these divergences thus enabling them\nto be good candidates for the description of the extension and the shape of\ncontinuous distributions. We apply this formalism to the projection of wave\nfunctions onto the coherent state basis, i.e. to the Husimi representation. We\nalso show how the localization properties of the Husimi distribution on average\ncan be reconstructed from its marginal distributions that are calculated in\nposition and momentum space in the case when the phase space has no structure,\ni.e. no classical limit can be defined. Numerical simulations on a one\ndimensional disordered system corroborate our expectations.", "category": "cond-mat_dis-nn" }, { "text": "Phase ordering on small-world networks with nearest-neighbor edges: We investigate global phase coherence in a system of coupled oscillators on a\nsmall-world networks constructed from a ring with nearest-neighbor edges. The\neffects of both thermal noise and quenched randomness on phase ordering are\nexamined and compared with the global coherence in the corresponding \\xy model\nwithout quenched randomness. It is found that in the appropriate regime phase\nordering emerges at finite temperatures, even for a tiny fraction of shortcuts.\nNature of the phase transition is also discussed.", "category": "cond-mat_dis-nn" }, { "text": "On the formal equivalence of the TAP and thermodynamic methods in the SK\n model: We revisit two classic Thouless-Anderson-Palmer (TAP) studies of the\nSherrington-Kirkpatrick model [Bray A J and Moore M A 1980 J. Phys. C 13, L469;\nDe Dominicis C and Young A P, 1983 J. Phys. A 16, 2063]. By using the\nBecchi-Rouet-Stora-Tyutin (BRST) supersymmetry, we prove the general\nequivalence of TAP and replica partition functions, and show that the annealed\ncalculation of the TAP complexity is formally identical to the quenched\nthermodynamic calculation of the free energy at one step level of replica\nsymmetry breaking. The complexity we obtain by means of the BRST symmetry turns\nout to be considerably smaller than the previous non-symmetric value.", "category": "cond-mat_dis-nn" }, { "text": "Laser Excitation of Polarization Waves in a Frozen Gas: Laser experiments with optically excited frozen gases entail the excitation\nof polarization waves. In a continuum approximation the waves are\ndispersionless, but their frequency depends on the direction of the propagation\nvector. An outline is given of the theory of transient phenomena that involve\nthe excitation of these waves by a resonant dipole-dipole transfer process.", "category": "cond-mat_dis-nn" }, { "text": "Spontaneous and stimulus-induced coherent states of critically balanced\n neuronal networks: How the information microscopically processed by individual neurons is\nintegrated and used in organizing the behavior of an animal is a central\nquestion in neuroscience. The coherence of neuronal dynamics over different\nscales has been suggested as a clue to the mechanisms underlying this\nintegration. Balanced excitation and inhibition may amplify microscopic\nfluctuations to a macroscopic level, thus providing a mechanism for generating\ncoherent multiscale dynamics. Previous theories of brain dynamics, however,\nwere restricted to cases in which inhibition dominated excitation and\nsuppressed fluctuations in the macroscopic population activity. In the present\nstudy, we investigate the dynamics of neuronal networks at a critical point\nbetween excitation-dominant and inhibition-dominant states. In these networks,\nthe microscopic fluctuations are amplified by the strong excitation and\ninhibition to drive the macroscopic dynamics, while the macroscopic dynamics\ndetermine the statistics of the microscopic fluctuations. Developing a novel\ntype of mean-field theory applicable to this class of interscale interactions,\nwe show that the amplification mechanism generates spontaneous, irregular\nmacroscopic rhythms similar to those observed in the brain. Through the same\nmechanism, microscopic inputs to a small number of neurons effectively entrain\nthe dynamics of the whole network. These network dynamics undergo a\nprobabilistic transition to a coherent state, as the magnitude of either the\nbalanced excitation and inhibition or the external inputs is increased. Our\nmean-field theory successfully predicts the behavior of this model.\nFurthermore, we numerically demonstrate that the coherent dynamics can be used\nfor state-dependent read-out of information from the network. These results\nshow a novel form of neuronal information processing that connects neuronal\ndynamics on different scales.", "category": "cond-mat_dis-nn" }, { "text": "Experimental Studies of Artificial Spin Ice: Artificial spin ices were originally introduced as analogs of the pyrochlore\nspin ices, but have since become a much richer field . The original attraction\nof building nanotechnological analogs of the pyrochlores were threefold: to\nallow room temperature studies of geometrical frustration; to provide model\nstatistical mechanical systems where all the relevant parameters in an\nexperiment can be tuned by design; and to be able to examine the exact\nmicrostate of those systems using advanced magnetic microscopy methods. From\nthis beginning the field has grown to encompass studies of the effects of\nquenched disorder, thermally activated dynamics, microwave frequency responses,\nmagnetotransport properties, and the development of lattice geometries--with\nrelated emergent physics---that have no analog in naturally-occurring\ncrystalline systems. The field also offers the prospect of contributing to\nnovel magnetic logic devices, since the arrays of nanoislands that form\nartificial spin ices are similar in many respects to those that are used in the\ndevelopment of magnetic quantum cellular automata. In this chapter, I review\nthe experimental aspects of this story, complementing the theoretical chapter\nby Gia-Wei Chern.", "category": "cond-mat_dis-nn" }, { "text": "Critical scaling in random-field systems: 2 or 3 independent exponents?: We show that the critical scaling behavior of random-field systems with\nshort-range interactions and disorder correlations cannot be described in\ngeneral by only two independent exponents, contrary to previous claims. This\nconclusion is based on a theoretical description of the whole (d,N) domain of\nthe d-dimensional random-field O(N) model and points to the role of rare events\nthat are overlooked by the proposed derivations of two-exponent scaling. Quite\nstrikingly, however, the numerical estimates of the critical exponents of the\nrandom field Ising model are extremely close to the predictions of the\ntwo-exponent scaling, so that the issue cannot be decided on the basis of\nnumerical simulations.", "category": "cond-mat_dis-nn" }, { "text": "Mean field theory for the three-dimensional Coulomb glass: We study the low temperature phase of the 3D Coulomb glass within a mean\nfield approach which reduces the full problem to an effective single site model\nwith a non-trivial replica structure. We predict a finite glass transition\ntemperature $T_c$, and a glassy low temperature phase characterized by\npermanent criticality. The latter is shown to assure the saturation of the\nEfros-Shklovskii Coulomb gap in the density of states. We find this pseudogap\nto be universal due to a fixed point in Parisi's flow equations. The latter is\ngiven a physical interpretation in terms of a dynamical self-similarity of the\nsystem in the long time limit, shedding new light on the concept of effective\ntemperature. From the low temperature solution we infer properties of the\nhierarchical energy landscape, which we use to make predictions about the\nmaster function governing the aging in relaxation experiments.", "category": "cond-mat_dis-nn" }, { "text": "Direct sampling of complex landscapes at low temperatures: the\n three-dimensional +/-J Ising spin glass: A method is presented, which allows to sample directly low-temperature\nconfigurations of glassy systems, like spin glasses. The basic idea is to\ngenerate ground states and low lying excited configurations using a heuristic\nalgorithm. Then, with the help of microcanonical Monte Carlo simulations, more\nconfigurations are found, clusters of configurations are determined and\nentropies evaluated. Finally equilibrium configuration are randomly sampled\nwith proper Gibbs-Boltzmann weights.\n The method is applied to three-dimensional Ising spin glasses with +- J\ninteractions and temperatures T<=0.5. The low-temperature behavior of this\nmodel is characterized by evaluating different overlap quantities, exhibiting a\ncomplex low-energy landscape for T>0, while the T=0 behavior appears to be less\ncomplex.", "category": "cond-mat_dis-nn" }, { "text": "Fluctuation-Induced Interactions and the Spin Glass Transition in\n $Fe_2TiO_5$: We investigate the spin-glass transition in the strongly frustrated\nwell-known compound $Fe_2TiO_5$. A remarkable feature of this transition,\nwidely discussed in the literature, is its anisotropic properties: the\ntransition manifests itself in the magnetic susceptibly only along one axis,\ndespite $Fe^{3+}$ $d^5$ spins having no orbital component. We demonstrate,\nusing neutron scattering, that below the transition temperature $T_g = 55 K$,\n$Fe_2TiO_5$ develops nanoscale surfboard shaped antiferromagnetic regions in\nwhich the $Fe^{3+}$ spins are aligned perpendicular to the axis which exhibits\nfreezing. We show that the glass transition may result from the freezing of\ntransverse fluctuations of the magnetization of these regions and we develop a\nmean-field replica theory of such a transition, revealing a type of magnetic\nvan der Waals effect.", "category": "cond-mat_dis-nn" }, { "text": "Non-Gaussian effects and multifractality in the Bragg glass: We study, beyond the Gaussian approximation, the decay of the translational\norder correlation function for a d-dimensional scalar periodic elastic system\nin a disordered environment. We develop a method based on functional\ndeterminants, equivalent to summing an infinite set of diagrams. We obtain, in\ndimension d=4-epsilon, the even n-th cumulant of relative displacements as\n<[u(r)-u(0)]^n>^c = A_n ln r, with A_n = -(\\epsilon/3)^n \\Gamma(n-1/2)\n\\zeta(2n-3)/\\pi^(1/2), as well as the multifractal dimension x_q of the\nexponential field e^{q u(r)}. As a corollary, we obtain an analytic expression\nfor a class of n-loop integrals in d=4, which appear in the perturbative\ndetermination of Konishi amplitudes, also accessible via AdS/CFT using\nintegrability.", "category": "cond-mat_dis-nn" }, { "text": "Universal Features of Terahertz Absorption in Disordered Materials: Using an analytical theory, experimental terahertz time-domain spectroscopy\ndata and numerical evidence, we demonstrate that the frequency dependence of\nthe absorption coupling coefficient between far-infrared photons and atomic\nvibrations in disordered materials has the universal functional form, C(omega)\n= A + B*omega^2, where the material-specific constants A and B are related to\nthe distributions of fluctuating charges obeying global and local charge\nneutrality, respectively.", "category": "cond-mat_dis-nn" }, { "text": "Magnetic dot arrays modeling via the system of the radial basis function\n networks: Two dimensional square lattice general model of the magnetic dot array is\nintroduced. In this model the intradot self-energy is predicted via the neural\nnetwork and interdot magnetostatic coupling is approximated by the collection\nof several dipolar terms. The model has been applied to disk-shaped cluster\ninvolving 193 ultrathin dots and 772 interaction centers. In this case among\nthe intradot magnetic structures retrieved by neural networks the important\nrole play single-vortex magnetization modes. Several aspects of the model have\nbeen understood numerically by means of the simulated annealing method.", "category": "cond-mat_dis-nn" }, { "text": "Statistics of cycles in large networks: We present a Markov Chain Monte Carlo method for sampling cycle length in\nlarge graphs. Cycles are treated as microstates of a system with many degrees\nof freedom. Cycle length corresponds to energy such that the length histogram\nis obtained as the density of states from Metropolis sampling. In many growing\nnetworks, mean cycle length increases algebraically with system size. The cycle\nexponent $\\alpha$ is characteristic of the local growth rules and not\ndetermined by the degree exponent $\\gamma$. For example, $\\alpha=0.76(4)$ for\nthe Internet at the Autonomous Systems level.", "category": "cond-mat_dis-nn" }, { "text": "Bath-induced decay of Stark many-body localization: We investigate the relaxation dynamics of an interacting Stark-localized\nsystem coupled to a dephasing bath, and compare its behavior to the\nconventional disorder-induced many body localized system. Specifically, we\nstudy the dynamics of population imbalance between even and odd sites, and the\ngrowth of the von Neumann entropy. For a large potential gradient, the\nimbalance is found to decay on a time scale that grows quadratically with the\nWannier-Stark tilt. For the non-interacting system, it shows an exponential\ndecay, which becomes a stretched exponential decay in the presence of finite\ninteractions. This is different from a system with disorder-induced\nlocalization, where the imbalance exhibits a stretched exponential decay also\nfor vanishing interactions. As another clear qualitative difference, we do not\nfind a logarithmically slow growth of the von-Neumann entropy as it is found\nfor the disordered system. Our findings can immediately be tested\nexperimentally with ultracold atoms in optical lattices.", "category": "cond-mat_dis-nn" }, { "text": "Continuum Field Model of Street Canyon: Theoretical Description; Part I: A general proecological urban road traffic control idea for the street canyon\nis proposed with emphasis placed on development of advanced continuum field\ngasdynamical (hydrodynamical) control model of the street canyon. The continuum\nfield model of optimal control of street canyon is studied. The mathematical\nphysics' approach (Eulerian approach) to vehicular movement, to pollutants'\nemission, and to pollutants' dynamics is used. The rigorous mathematical model\nis presented, using gasdynamical (hydrodynamical) theory for both air\nconstituents and vehicles, including many types of vehicles and many types of\npollutant (exhaust gases) emitted from vehicles. The six optimal control\nproblems are formulated.", "category": "cond-mat_dis-nn" }, { "text": "Critical behaviour and ultrametricity of Ising spin-glass with\n long-range interactions: Ising spin-glass systems with long-range interactions ($J(r)\\sim\nr^{-\\sigma}$) are considered. A numerical study of the critical behaviour is\npresented in the non-mean-field region together with an analysis of the\nprobability distribution of the overlaps and of the ultrametric structure of\nthe space of the equilibrium configurations in the frozen phase. Also in\npresence of diverging thermodynamical fluctuations at the critical point the\nbehaviour of the model is shown to be of the Replica Simmetry Breaking type and\nthere are hints of a non-trivial ultrametric structure. The parallel tempering\nalgorithm has been used to simulate the dynamical approach to equilibrium of\nsuch systems.", "category": "cond-mat_dis-nn" }, { "text": "Localization and delocalization in one-dimensional systems with\n translation-invariant hopping: We present a theory of Anderson localization on a one-dimensional lattice\nwith translation-invariant hopping. We find by analytical calculation, the\nlocalization length for arbitrary finite-range hopping in the single\npropagating channel regime. Then by examining the convergence of the\nlocalization length, in the limit of infinite hopping range, we revisit the\nproblem of localization criteria in this model and investigate the conditions\nunder which it can be violated. Our results reveal possibilities of having\ndelocalized states by tuning the long-range hopping.", "category": "cond-mat_dis-nn" }, { "text": "Probing spin glasses with heuristic optimization algorithms: A sketch of the chapter appearing under the same heading in the book ``New\nOptimization Algorithms in Physics'' (A.K. Hartmann and H. Rieger, Eds.) is\ngiven. After a general introduction to spin glasses, important aspects of\nheuristic algorithms for tackling these systems are covered. Some open problems\nthat one can hope to resolve in the next few years are then considered.", "category": "cond-mat_dis-nn" }, { "text": "Specific Heat of Quantum Elastic Systems Pinned by Disorder: We present the detailed study of the thermodynamics of vibrational modes in\ndisordered elastic systems such as the Bragg glass phase of lattices pinned by\nquenched impurities. Our study and our results are valid within the (mean\nfield) replica Gaussian variational method. We obtain an expression for the\ninternal energy in the quantum regime as a function of the saddle point\nsolution, which is then expanded in powers of $\\hbar$ at low temperature $T$.\nIn the calculation of the specific heat $C_v$ a non trivial cancellation of the\nterm linear in $T$ occurs, explicitly checked to second order in $\\hbar$. The\nfinal result is $C_v \\propto T^3$ at low temperatures in dimension three and\ntwo. The prefactor is controlled by the pinning length. This result is\ndiscussed in connection with other analytical or numerical studies.", "category": "cond-mat_dis-nn" }, { "text": "Heterogeneous dynamics of the three dimensional Coulomb glass out of\n equilibrium: The non-equilibrium relaxational properties of a three dimensional Coulomb\nglass model are investigated by kinetic Monte Carlo simulations. Our results\nsuggest a transition from stationary to non-stationary dynamics at the\nequilibrium glass transition temperature of the system. Below the transition\nthe dynamic correlation functions loose time translation invariance and\nelectron diffusion is anomalous. Two groups of carriers can be identified at\neach time scale, electrons whose motion is diffusive within a selected time\nwindow and electrons that during the same time interval remain confined in\nsmall regions in space. During the relaxation that follows a temperature quench\nan exchange of electrons between these two groups takes place and the\nnon-equilibrium excess of diffusive electrons initially present decreases\nlogarithmically with time as the system relaxes. This bimodal dynamical\nheterogeneity persists at higher temperatures when time translation invariance\nis restored and electron diffusion is normal. The occupancy of the two\ndynamical modes is then stationary and its temperature dependence reflects a\ncrossover between a low-temperature regime with a high concentration of\nelectrons forming fluctuating dipoles and a high-temperature regime in which\nthe concentration of diffusive electrons is high.", "category": "cond-mat_dis-nn" }, { "text": "Random transverse-field Ising chain with long-range interactions: We study the low-energy properties of the long-range random transverse-field\nIsing chain with ferromagnetic interactions decaying as a power alpha of the\ndistance. Using variants of the strong-disorder renormalization group method,\nthe critical behavior is found to be controlled by a strong-disorder fixed\npoint with a finite dynamical exponent z_c=alpha. Approaching the critical\npoint, the correlation length diverges exponentially. In the critical point,\nthe magnetization shows an alpha-independent logarithmic finite-size scaling\nand the entanglement entropy satisfies the area law. These observations are\nargued to hold for other systems with long-range interactions, even in higher\ndimensions.", "category": "cond-mat_dis-nn" }, { "text": "Localization properties of the asymptotic density distribution of a\n one-dimensional disordered system: Anderson localization is the ubiquitous phenomenon of inhibition of transport\nof classical and quantum waves in a disordered medium. In dimension one, it is\nwell known that all states are localized, implying that the distribution of an\ninitially narrow wave-packet released in a disordered potential will, at long\ntime, decay exponentially on the scale of the localization length. However, the\nexact shape of the stationary localized distribution differs from a purely\nexponential profile and has been computed almost fifty years ago by Gogolin.\n Using the atomic quantum kicked rotor, a paradigmatic quantum simulator of\nAnderson localization physics, we study this asymptotic distribution by two\ncomplementary approaches. First, we discuss the connection of the statistical\nproperties of the system's localized eigenfunctions and their exponential decay\nwith the localization length of the Gogolin distribution. Next, we make use of\nour experimental platform, realizing an ideal Floquet disordered system, to\nmeasure the long-time probability distribution and highlight the very good\nagreement with the analytical prediction compared to the purely exponential one\nover 3 orders of magnitude.", "category": "cond-mat_dis-nn" }, { "text": "Correlation length of the two-dimensional Ising spin glass with bimodal\n interactions: We study the correlation length of the two-dimensional Edwards-Anderson Ising\nspin glass with bimodal interactions using a combination of parallel tempering\nMonte Carlo and a rejection-free cluster algorithm in order to speed up\nequilibration. Our results show that the correlation length grows ~ exp(2J/T)\nsuggesting through hyperscaling that the degenerate ground state is separated\nfrom the first excited state by an energy gap ~4J, as would naively be\nexpected.", "category": "cond-mat_dis-nn" }, { "text": "Memories of initial states and density imbalance in dynamics of\n interacting disordered systems: We study the dynamics of one and two dimensional disordered lattice\nbosons/fermions initialized to a Fock state with a pattern of $1$ and $0$\nparticles on $A$ and ${\\bar A}$ sites. For non-interacting systems we establish\na universal relation between the long time density imbalance between $A$ and\n${\\bar A}$ site, $I(\\infty)$, the localization length $\\xi_l$, and the geometry\nof the initial pattern. For alternating initial pattern of $1$ and $0$\nparticles in 1 dimension, $I(\\infty)=\\tanh[a/\\xi_l]$, where $a$ is the lattice\nspacing. For systems with mobility edge, we find analytic relations between\n$I(\\infty)$, the effective localization length $\\tilde{\\xi}_l$ and the fraction\nof localized states $f_l$. The imbalance as a function of disorder shows\nnon-analytic behaviour when the mobility edge passes through a band edge. For\ninteracting bosonic systems, we show that dissipative processes lead to a decay\nof the memory of initial conditions. However, the excitations created in the\nprocess act as a bath, whose noise correlators retain information of the\ninitial pattern. This sustains a finite imbalance at long times in strongly\ndisordered interacting systems.", "category": "cond-mat_dis-nn" }, { "text": "Resonant metallic states in driven quasiperiodic lattices: We consider a quasiperiodic Aubry-Andre (AA) model and add a weak\ntime-periodic and spatially quasiperiodic perturbation. The undriven AA model\nis chosen to be well in the insulating regime. The spatial quasiperiodic\nperturbation extends the model into two dimensions in reciprocal space. For a\nspatial resonance which reduces the reciprocal space dynamics to an effective\none-dimensional two-leg ladder case, the ac perturbation resonantly couples\ncertain groups of localized eigenstates of the undriven AA model and turns them\ninto extended metallic ones. Slight detuning of the spatial and temporal\nfrequencies off resonance returns these states into localized ones. We analyze\nthe details of the resonant metallic eigenstates using Floquet representations.\nIn particular, we find that their size grows linearly with the system size.\nInitial wave packets overlap with resonant metallic eigenstates and lead to\nballistic spreading.", "category": "cond-mat_dis-nn" }, { "text": "Method to solve quantum few-body problems with artificial neural\n networks: A machine learning technique to obtain the ground states of quantum few-body\nsystems using artificial neural networks is developed. Bosons in continuous\nspace are considered and a neural network is optimized in such a way that when\nparticle positions are input into the network, the ground-state wave function\nis output from the network. The method is applied to the Calogero-Sutherland\nmodel in one-dimensional space and Efimov bound states in three-dimensional\nspace.", "category": "cond-mat_dis-nn" }, { "text": "Evidence for existence of many pure ground states in 3d $\\pm J$ Spin\n Glasses: Ground states of 3d EA Ising spin glasses are calculated for sizes up to\n$14^3$ using a combination of genetic algorithms and cluster-exact\napproximation . The distribution $P(|q|)$ of overlaps is calculated. For\nincreasing size the width of $P(|q|)$ converges to a nonzero value, indicating\nthat many pure ground states exist for short range Ising spin glasses.", "category": "cond-mat_dis-nn" }, { "text": "The number of guards needed by a museum: A phase transition in vertex\n covering of random graphs: In this letter we study the NP-complete vertex cover problem on finite\nconnectivity random graphs. When the allowed size of the cover set is\ndecreased, a discontinuous transition in solvability and typical-case\ncomplexity occurs. This transition is characterized by means of exact numerical\nsimulations as well as by analytical replica calculations. The replica\nsymmetric phase diagram is in excellent agreement with numerical findings up to\naverage connectivity $e$, where replica symmetry becomes locally unstable.", "category": "cond-mat_dis-nn" }, { "text": "Testing a Variational Approach to Random Directed Polymers: The one dimensional direct polymer in random media model is investigated\nusing a variational approach in the replica space. We demonstrate numerically\nthat the stable point is a maximum and the corresponding statistical properties\nfor the delta correlated potential are in good agreements with the known\nanalytic solution. In the case of power-law correlated potential two regimes\nare recovered: a Flory scaling dependent on the exponent of the correlations,\nand a short range regime in analogy with the delta-correlated potential case.", "category": "cond-mat_dis-nn" }, { "text": "Comment on \"Disorder Induced Quantum Phase Transition in Random-Exchange\n Spin-1/2 Chains\": We reconsider the random bond antiferromagnetic spin-1/2 chain for weak\ndisorder and demonstrate the existence of crossover length scale x_W that\ndiverges with decreasing strength of the disorder. Recent DMRG calculations\n[Phys. Rev. Lett. 89, 127202 (2002); cond-mat/0111027] claimed to have found\nevidence for a non-universal behavior in this model and found no indications of\na universal infinite randomness fixed point (IRFP) scenario. We show that these\ndata are not in the asymptotic regime since the system sizes that have been\nconsidered are of the same order of magnitude or much smaller than the\ncrossover length x_W. We give a scaling form for the xx-spin-correlation\nfunction that takes this crossover length into account and that is compatible\nwith the IRFP scenario and a random singlet phase.", "category": "cond-mat_dis-nn" }, { "text": "Atomic level structure of Ge-Sb-S glasses: chemical short range order\n and long Sb-S bonds: The structure of Ge$_{20}$Sb$_{10}$S$_{70}$, Ge$_{23}$Sb$_{12}$S$_{65}$ and\nGe$_{26}$Sb$_{13}$S$_{61}$ glasses was investigated by neutron diffraction\n(ND), X-ray diffraction (XRD), extended X-ray absorption fine structure (EXAFS)\nmeasurements at the Ge and Sb K-edges as well as Raman scattering. For each\ncomposition, large scale structural models were obtained by fitting\nsimultaneously diffraction and EXAFS data sets in the framework of the reverse\nMonte Carlo (RMC) simulation technique. Ge and S atoms have 4 and 2 nearest\nneighbors, respectively. The structure of these glasses can be described by the\nchemically ordered network model: Ge-S and Sb-S bonds are always preferred.\nThese two bond types adequately describe the structure of the stoichiometric\nglass while S-S bonds can also be found in the S-rich composition. Raman\nscattering data show the presence of Ge-Ge, Ge-Sb and Sb-Sb bonds in the\nS-deficient glass but only Ge-Sb bonds are needed to fit diffraction and EXAFS\ndatasets. A significant part of the Sb-S pairs has 0.3-0.4 {\\AA} longer bond\ndistance than the usually accepted covalent bond length (~2.45 {\\AA}). From\nthis observation it was inferred that a part of Sb atoms have more than 3 S\nneighbors.", "category": "cond-mat_dis-nn" }, { "text": "Polaritons in 2D-crystals and localized modes in narrow waveguides: We study 2D-polaritons in an atomically thin dipole-active layer (2D-crystal)\nplaced inside a parallel-plate wavegude, and investigate the possibility to\nobtain the localized wavegude modes associated with atomic defects. Considering\nthe wavegude width, $l,$ as an adjustable parameter, we show that in the\nwaveguide with $l\\sim 10^{4} a,$ where $a$ is the lattice parameter, the\nlocalized mode can be provided by a single impurity or a local structural\ndefect.", "category": "cond-mat_dis-nn" }, { "text": "Mean Field Theory of the Three-Dimensional Dipole Superspin Glasses: We study the three-dimensional system of magnetic nanoparticle dipoles\nrandomly oriented along quenched easy axes. Directions of the magnetic momenta\nare described by the Ising variables which allow the momenta to flip along\ntheir random orientations. Using the standard mean-field approximation and the\nreplica technique it is shown that the system undergoes a finite temperature\nphase transition into a spin-glass phase.", "category": "cond-mat_dis-nn" }, { "text": "Tunneling and Non-Universality in Continuum Percolation Systems: The values obtained experimentally for the conductivity critical exponent in\nnumerous percolation systems, in which the interparticle conduction is by\ntunnelling, were found to be in the range of $t_0$ and about $t_0+10$, where\n$t_0$ is the universal conductivity exponent. These latter values are however\nconsiderably smaller than those predicted by the available ``one\ndimensional\"-like theory of tunneling-percolation. In this letter we show that\nthis long-standing discrepancy can be resolved by considering the more\nrealistic \"three dimensional\" model and the limited proximity to the\npercolation threshold in all the many available experimental studies", "category": "cond-mat_dis-nn" }, { "text": "Origin of the computational hardness for learning with binary synapses: Supervised learning in a binary perceptron is able to classify an extensive\nnumber of random patterns by a proper assignment of binary synaptic weights.\nHowever, to find such assignments in practice, is quite a nontrivial task. The\nrelation between the weight space structure and the algorithmic hardness has\nnot yet been fully understood. To this end, we analytically derive the\nFranz-Parisi potential for the binary preceptron problem, by starting from an\nequilibrium solution of weights and exploring the weight space structure around\nit. Our result reveals the geometrical organization of the weight\nspace\\textemdash the weight space is composed of isolated solutions, rather\nthan clusters of exponentially many close-by solutions. The point-like clusters\nfar apart from each other in the weight space explain the previously observed\nglassy behavior of stochastic local search heuristics.", "category": "cond-mat_dis-nn" }, { "text": "Scaling hypothesis for the Euclidean bipartite matching problem II.\n Correlation functions: We analyze the random Euclidean bipartite matching problem on the hypertorus\nin $d$ dimensions with quadratic cost and we derive the two--point correlation\nfunction for the optimal matching, using a proper ansatz introduced by\nCaracciolo et al. to evaluate the average optimal matching cost. We consider\nboth the grid--Poisson matching problem and the Poisson--Poisson matching\nproblem. We also show that the correlation function is strictly related to the\nGreen's function of the Laplace operator on the hypertorus.", "category": "cond-mat_dis-nn" }, { "text": "Hidden dimers and the matrix maps: Fibonacci chains re-visited: The existence of cycles of the matrix maps in Fibonacci class of lattices is\nwell established. We show that such cycles are intimately connected with the\npresence of interesting positional correlations among the constituent `atoms'\nin a one dimensional quasiperiodic lattice. We particularly address the\ntransfer model of the classic golden mean Fibonacci chain where a six cycle of\nthe full matrix map exists at the centre of the spectrum [Kohmoto et al, Phys.\nRev. B 35, 1020 (1987)], and for which no simple physical picture has so far\nbeen provided, to the best of our knowledge. In addition, we show that our\nprescription leads to a determination of other energy values for a mixed model\nof the Fibonacci chain, for which the full matrix map may have similar cyclic\nbehaviour. Apart from the standard transfer-model of a golden mean Fibonacci\nchain, we address a variant of it and the silver mean lattice, where the\nexistence of four cycles of the matrix map is already known to exist. The\nunderlying positional correlations for all such cases are discussed in details.", "category": "cond-mat_dis-nn" }, { "text": "Numerical Solution-Space Analysis of Satisfiability Problems: The solution-space structure of the 3-Satisfiability Problem (3-SAT) is\nstudied as a function of the control parameter alpha (ratio of number of\nclauses to the number of variables) using numerical simulations. For this\npurpose, one has to sample the solution space with uniform weight. It is shown\nhere that standard stochastic local-search (SLS) algorithms like \"ASAT\" and\n\"MCMCMC\" (also known as \"parallel tempering\") exhibit a sampling bias.\nNevertheless, unbiased samples of solutions can be obtained using the\n\"ballistic-networking approach\", which is introduced here. It is a\ngeneralization of \"ballistic search\" methods and yields also a cluster\nstructure of the solution space. As application, solutions of 3-SAT instances\nare generated using ASAT plus ballistic networking. The numerical results are\ncompatible with a previous analytic prediction of a simple solution-space\nstructure for small values of alpha and a transition to a clustered phase at\nalpha_c ~ 3.86, where the solution space breaks up into several non-negligible\nclusters. Furthermore, in the thermodynamic limit there are, for values of\nalpha close to the SATUNSAT transition alpha_s ~ 4.267, always clusters without\nany frozen variables. This may explain why some SLS algorithms are able to\nsolve very large 3-SAT instances close to the SAT-UNSAT transition.", "category": "cond-mat_dis-nn" }, { "text": "Spatio-temporal correlations in Wigner molecules: The dynamical response of Coulomb-interacting particles in nano-clusters are\nanalyzed at different temperatures characterizing their solid- and liquid-like\nbehavior. Depending on the trap-symmetry, both the spatial and temporal\ncorrelations undergo slow, stretched exponential relaxations at long times,\narising from spatially correlated motion in string-like paths. Our results\nindicate that the distinction between the `solid' and `liquid' is soft: While\nparticles in a `solid' flow producing dynamic heterogeneities, motion in\n`liquid' yields unusually long tail in the distribution of\nparticle-displacements. A phenomenological model captures much of the\nsubtleties of our numerical simulations.", "category": "cond-mat_dis-nn" }, { "text": "Anisotropic Magnetoconductance in Quench-Condensed Ultrathin Beryllium\n Films: Near the superconductor-insulator (S-I) transition, quench-condensed\nultrathin Be films show a large magnetoconductance which is highly anisotropic\nin the direction of the applied field. Film conductance can drop as much as\nseven orders of magnitude in a weak perpendicular field (< 1 T), but is\ninsensitive to a parallel field in the same field range. We believe that this\nnegative magnetoconductance is due to the field de-phasing of the\nsuperconducting pair wavefunction. This idea enables us to extract the finite\nsuperconducting phase coherence length in nearly superconducting films. Our\ndata indicate that this local phase coherence persists even in highly\ninsulating films in the vicinity of the S-I transition.", "category": "cond-mat_dis-nn" }, { "text": "Short-range Magnetic interactions in the Spin-Ice compound\n Ho$_{2}$Ti$_{2}$O$_{7}$: Magnetization and susceptibility studies on single crystals of the pyrochlore\nHo$_{2}$Ti$_{2}$O$_{7}$ are reported for the first time. Magnetization\nisotherms are shown to be qualitatively similar to that predicted by the\nnearest neighbor spin-ice model. Below the lock-in temperature, $T^{\\ast\n}\\simeq 1.97$ K, magnetization is consistent with the locking of spins along\n[111] directions in a specific two-spins-in, two-spins-out arrangement. Below\n$T^{\\ast}$ the magnetization for $B||[111]$ displays a two step behavior\nsignalling the breaking of the ice rules.", "category": "cond-mat_dis-nn" }, { "text": "Chaos in Glassy Systems from a TAP Perspective: We discuss level crossing of the free-energy of TAP solutions under\nvariations of external parameters such as magnetic field or temperature in\nmean-field spin-glass models that exhibit one-step Replica-Symmetry-Breaking\n(1RSB). We study the problem through a generalized complexity that describes\nthe density of TAP solutions at a given value of the free-energy and a given\nvalue of the extensive quantity conjugate to the external parameter. We show\nthat variations of the external parameter by any finite amount can induce level\ncrossing between groups of TAP states whose free-energies are extensively\ndifferent. In models with 1RSB, this means strong chaos with respect to the\nperturbation. The linear-response induced by extensive level crossing is\nself-averaging and its value matches precisely with the disorder-average of the\nnon self-averaging anomaly computed from the 2nd moment of thermal fluctuations\nbetween low-lying, almost degenerate TAP states. We present an analytical\nrecipe to compute the generalized complexity and test the scenario on the\nspherical multi-$p$ spin models under variation of temperature.", "category": "cond-mat_dis-nn" }, { "text": "Modified spin-wave study of random antiferromagnetic-ferromagnetic spin\n chains: We study the thermodynamics of one-dimensional quantum spin-1/2 Heisenberg\nferromagnetic system with random antiferromagnetic impurity bonds. In the\ndilute impurity limit, we generalize the modified spin-wave theory for random\nspin chains, where local chemical potentials for spin-waves in ferromagnetic\nspin segments are introduced to ensure zero magnetization at finite\ntemperature. This approach successfully describes the crossover from behavior\nof pure one-dimensional ferromagnet at high temperatures to a distinct Curie\nbehavior due to randomness at low temperatures. We discuss the effects of\nimpurity bond strength and concentration on the crossover and low temperature\nbehavior.", "category": "cond-mat_dis-nn" }, { "text": "Spin-Glass Phase in the Random Temperature Ising Ferromagnet: In this paper we study the phase diagram of the disordered Ising ferromagnet.\nWithin the framework of the Gaussian variational approximation it is shown that\nin systems with a finite value of the disorder in dimensions D=4 and D < 4 the\nparamagnetic and ferromagnetic phases are separated by a spin-glass phase. The\ntransition from paramagnetic to spin-glass state is continuous (second-order),\nwhile the transition between spin-glass and ferromagnetic states is\ndiscontinuous (first-order). It is also shown that within the considered\napproximation there is no replica symmetry breaking in the spin-glass phase.\nThe validity of the Gaussian variational approximation for the present problem\nis discussed, and we provide a tentative physical interpretation of the\nresults.", "category": "cond-mat_dis-nn" }, { "text": "Phase transitions induced by microscopic disorder: a study based on the\n order parameter expansion: Based on the order parameter expansion, we present an approximate method\nwhich allows us to reduce large systems of coupled differential equations with\ndiverse parameters to three equations: one for the global, mean field, variable\nand two which describe the fluctuations around this mean value. With this tool\nwe analyze phase-transitions induced by microscopic disorder in three\nprototypical models of phase-transitions which have been studied previously in\nthe presence of thermal noise. We study how macroscopic order is induced or\ndestroyed by time independent local disorder and analyze the limits of the\napproximation by comparing the results with the numerical solutions of the\nself-consistency equation which arises from the property of self-averaging.\nFinally, we carry on a finite-size analysis of the numerical results and\ncalculate the corresponding critical exponents.", "category": "cond-mat_dis-nn" }, { "text": "Are Mean-Field Spin-Glass Models Relevant for the Structural Glass\n Transition?: We analyze the properties of the energy landscape of {\\it finite-size} fully\nconnected p-spin-like models whose high temperature phase is described, in the\nthermodynamic limit, by the schematic Mode Coupling Theory of super-cooled\nliquids. We show that {\\it finite-size} fully connected p-spin-like models,\nwhere activated processes are possible, do exhibit properties typical of real\nsuper-cooled liquid when both are near the critical glass transition. Our\nresults support the conclusion that fully-connected p-spin-like models are the\nnatural statistical mechanical models for studying the glass transition in\nsuper-cooled liquids.", "category": "cond-mat_dis-nn" }, { "text": "Curie Temperature for Small World Ising Systems of Different Dimensions: For Small World Ising systems of different dimensions, \"concentration\"\ndependencies T_C(p) of the Curie temperature upon the fraction p of long-range\nlinks have been derived on a basis of simple physical considerations. We have\nfound T_C(p) ~ 1/ln|p| for 1D, T_C(p) ~ p^{1/2} for 2D, and T_C(p) ~ p^{2/3}\nfor 3D.", "category": "cond-mat_dis-nn" }, { "text": "The Centred Traveling Salesman at Finite Temperature: A recently formulated statistical mechanics method is used to study the phase\ntransition occurring in a generalisation of the Traveling Salesman Problem\n(TSP) known as the centred TSP. The method shows that the problem has clear\nsigns of a crossover, but is only able to access (unscaled) finite temperatures\nabove the transition point. The solution of the problem using this method\ndisplays a curious duality.", "category": "cond-mat_dis-nn" }, { "text": "Fluctuations analysis in complex networks modeled by hidden variable\n models. Necessity of a large cut-off in hidden-variable models: It is becoming more and more clear that complex networks present remarkable\nlarge fluctuations. These fluctuations may manifest differently according to\nthe given model. In this paper we re-consider hidden variable models which turn\nout to be more analytically treatable and for which we have recently shown\nclear evidence of non-self averaging; the density of a motif being subject to\npossible uncontrollable fluctuations in the infinite size limit. Here we\nprovide full detailed calculations and we show that large fluctuations are only\ndue to the node hidden variables variability while, in ensembles where these\nare frozen, fluctuations are negligible in the thermodynamic limit, and equal\nthe fluctuations of classical random graphs. A special attention is paid to the\nchoice of the cut-off: we show that in hidden-variable models, only a cut-off\ngrowing as $N^\\lambda$ with $\\lambda\\geq 1$ can reproduce the scaling of a\npower-law degree distribution. In turn, it is this large cut-off that generates\nnon-self-averaging.", "category": "cond-mat_dis-nn" }, { "text": "Critical dynamics of the k-core pruning process: We present the theory of the k-core pruning process (progressive removal of\nnodes with degree less than k) in uncorrelated random networks. We derive exact\nequations describing this process and the evolution of the network structure,\nand solve them numerically and, in the critical regime of the process,\nanalytically. We show that the pruning process exhibits three different\nbehaviors depending on whether the mean degree of the initial network is\nabove, equal to, or below the threshold _c corresponding to the emergence of\nthe giant k-core. We find that above the threshold the network relaxes\nexponentially to the k-core. The system manifests the phenomenon known as\n\"critical slowing down\", as the relaxation time diverges when tends to\n_c. At the threshold, the dynamics become critical characterized by a\npower-law relaxation (1/t^2). Below the threshold, a long-lasting transient\nprocess (a \"plateau\" stage) occurs. This transient process ends with a collapse\nin which the entire network disappears completely. The duration of the process\ndiverges when tends to _c. We show that the critical dynamics of the\npruning are determined by branching processes of spreading damage. Clusters of\nnodes of degree exactly k are the evolving substrate for these branching\nprocesses. Our theory completely describes this branching cascade of damage in\nuncorrelated networks by providing the time dependent distribution function of\nbranching. These theoretical results are supported by our simulations of the\n$k$-core pruning in Erdos-Renyi graphs.", "category": "cond-mat_dis-nn" }, { "text": "Effects of substrate network topologies on competition dynamics: We study a competition dynamics, based on the minority game, endowed with\nvarious substrate network structures. We observe the effects of the network\ntopologies by investigating the volatility of the system and the structure of\nfollower networks. The topology of substrate structures significantly\ninfluences the system efficiency represented by the volatility and such\nsubstrate networks are shown to amplify the herding effect and cause\ninefficiency in most cases. The follower networks emerging from the leadership\nstructure show a power-law incoming degree distribution. This study shows the\nemergence of scale-free structures of leadership in the minority game and the\neffects of the interaction among players on the networked version of the game.", "category": "cond-mat_dis-nn" }, { "text": "The Physics of Living Neural Networks: Improvements in technique in conjunction with an evolution of the theoretical\nand conceptual approach to neuronal networks provide a new perspective on\nliving neurons in culture. Organization and connectivity are being measured\nquantitatively along with other physical quantities such as information, and\nare being related to function. In this review we first discuss some of these\nadvances, which enable elucidation of structural aspects. We then discuss two\nrecent experimental models that yield some conceptual simplicity. A\none-dimensional network enables precise quantitative comparison to analytic\nmodels, for example of propagation and information transport. A two-dimensional\npercolating network gives quantitative information on connectivity of cultured\nneurons. The physical quantities that emerge as essential characteristics of\nthe network in vitro are propagation speeds, synaptic transmission, information\ncreation and capacity. Potential application to neuronal devices is discussed.", "category": "cond-mat_dis-nn" }, { "text": "Statistical Mechanics of the Bayesian Image Restoration under Spatially\n Correlated Noise: We investigated the use of the Bayesian inference to restore noise-degraded\nimages under conditions of spatially correlated noise. The generative\nstatistical models used for the original image and the noise were assumed to\nobey multi-dimensional Gaussian distributions whose covariance matrices are\ntranslational invariant. We derived an exact description to be used as the\nexpectation for the restored image by the Fourier transformation and restored\nan image distorted by spatially correlated noise by using a spatially\nuncorrelated noise model. We found that the resulting hyperparameter\nestimations for the minimum error and maximal posterior marginal criteria did\nnot coincide when the generative probabilistic model and the model used for\nrestoration were in different classes, while they did coincide when they were\nin the same class.", "category": "cond-mat_dis-nn" }, { "text": "Interpolating between boolean and extremely high noisy patterns through\n Minimal Dense Associative Memories: Recently, Hopfield and Krotov introduced the concept of {\\em dense\nassociative memories} [DAM] (close to spin-glasses with $P$-wise interactions\nin a disordered statistical mechanical jargon): they proved a number of\nremarkable features these networks share and suggested their use to (partially)\nexplain the success of the new generation of Artificial Intelligence. Thanks to\na remarkable ante-litteram analysis by Baldi \\& Venkatesh, among these\nproperties, it is known these networks can handle a maximal amount of stored\npatterns $K$ scaling as $K \\sim N^{P-1}$.\\\\ In this paper, once introduced a\n{\\em minimal dense associative network} as one of the most elementary\ncost-functions falling in this class of DAM, we sacrifice this high-load regime\n-namely we force the storage of {\\em solely} a linear amount of patterns, i.e.\n$K = \\alpha N$ (with $\\alpha>0$)- to prove that, in this regime, these networks\ncan correctly perform pattern recognition even if pattern signal is $O(1)$ and\nis embedded in a sea of noise $O(\\sqrt{N})$, also in the large $N$ limit. To\nprove this statement, by extremizing the quenched free-energy of the model over\nits natural order-parameters (the various magnetizations and overlaps), we\nderived its phase diagram, at the replica symmetric level of description and in\nthe thermodynamic limit: as a sideline, we stress that, to achieve this task,\naiming at cross-fertilization among disciplines, we pave two hegemon routes in\nthe statistical mechanics of spin glasses, namely the replica trick and the\ninterpolation technique.\\\\ Both the approaches reach the same conclusion: there\nis a not-empty region, in the noise-$T$ vs load-$\\alpha$ phase diagram plane,\nwhere these networks can actually work in this challenging regime; in\nparticular we obtained a quite high critical (linear) load in the (fast)\nnoiseless case resulting in $\\lim_{\\beta \\to \\infty}\\alpha_c(\\beta)=0.65$.", "category": "cond-mat_dis-nn" }, { "text": "Analytic Solution to Clustering Coefficients on Weighted Networks: Clustering coefficient is an important topological feature of complex\nnetworks. It is, however, an open question to give out its analytic expression\non weighted networks yet. Here we applied an extended mean-field approach to\ninvestigate clustering coefficients in the typical weighted networks proposed\nby Barrat, Barth\\'elemy and Vespignani (BBV networks). We provide analytical\nsolutions of this model and find that the local clustering in BBV networks\ndepends on the node degree and strength. Our analysis is well in agreement with\nresults of numerical simulations.", "category": "cond-mat_dis-nn" }, { "text": "Direct topological insulator transitions in three dimensions are\n destabilized by non-perturbative effects of disorder: We reconsider the phase diagram of a three-dimensional $\\mathbb{Z}_2$\ntopological insulator in the presence of short-ranged potential disorder with\nthe insight that non-perturbative rare states destabilize the noninteracting\nDirac semimetal critical point separating different topological phases. Based\non our numerical data on the density of states, conductivity, and\nwavefunctions, we argue that the putative Dirac semimetal line is destabilized\ninto a diffusive metal phase of finite extent due to non-perturbative effects\nof rare regions. We discuss the implications of these results for past and\ncurrent experiments on doped topological insulators.", "category": "cond-mat_dis-nn" }, { "text": "Structure and Time-Evolution of an Internet Dating Community: We present statistics for the structure and time-evolution of a network\nconstructed from user activity in an Internet community. The vastness and\nprecise time resolution of an Internet community offers unique possibilities to\nmonitor social network formation and dynamics. Time evolution of well-known\nquantities, such as clustering, mixing (degree-degree correlations), average\ngeodesic length, degree, and reciprocity is studied. In contrast to earlier\nanalyses of scientific collaboration networks, mixing by degree between\nvertices is found to be disassortative. Furthermore, both the evolutionary\ntrajectories of the average geodesic length and of the clustering coefficients\nare found to have minima.", "category": "cond-mat_dis-nn" }, { "text": "Monte Carlo studies of the one-dimensional Ising spin glass with\n power-law interactions: We present results from Monte Carlo simulations of the one-dimensional Ising\nspin glass with power-law interactions at low temperature, using the parallel\ntempering Monte Carlo method. For a set of parameters where the long-range part\nof the interaction is relevant, we find evidence for large-scale droplet-like\nexcitations with an energy that is independent of system size, consistent with\nreplica symmetry breaking. We also perform zero-temperature defect energy\ncalculations for a range of parameters and find a stiffness exponent for domain\nwalls in reasonable, but by no means perfect agreement with analytic\npredictions.", "category": "cond-mat_dis-nn" }, { "text": "Properties of equilibria and glassy phases of the random Lotka-Volterra\n model with demographic noise: In this letter we study a reference model in theoretical ecology, the\ndisordered Lotka-Volterra model for ecological communities, in the presence of\nfinite demographic noise. Our theoretical analysis, which takes advantage of a\nmapping to an equilibrium disordered system, proves that for sufficiently\nheterogeneous interactions and low demographic noise the system displays a\nmultiple equilibria phase, which we fully characterize. In particular, we show\nthat in this phase the number of stable equilibria is exponential in the number\nof species. Upon further decreasing the demographic noise, we unveil a\n\"Gardner\" transition to a marginally stable phase, similar to that observed in\njamming of amorphous materials. We confirm and complement our analytical\nresults by numerical simulations. Furthermore, we extend their relevance by\nshowing that they hold for others interacting random dynamical systems, such as\nthe Random Replicant Model. Finally, we discuss their extension to the case of\nasymmetric couplings.", "category": "cond-mat_dis-nn" }, { "text": "Weakly driven anomalous diffusion in non-ergodic regime: an analytical\n solution: We derive the probability density of a diffusion process generated by\nnonergodic velocity fluctuations in presence of a weak potential, using the\nLiouville equation approach. The velocity of the diffusing particle undergoes\ndichotomic fluctuations with a given distribution $\\psi(\\tau)$ of residence\ntimes in each velocity state. We obtain analytical solutions for the diffusion\nprocess in a generic external potential and for a generic statistics of\nresidence times, including the non-ergodic regime in which the mean residence\ntime diverges. We show that these analytical solutions are in agreement with\nnumerical simulations.", "category": "cond-mat_dis-nn" }, { "text": "Study of off-diagonal disorder using the typical medium dynamical\n cluster approximation: We generalize the typical medium dynamical cluster approximation (TMDCA) and\nthe local Blackman, Esterling, and Berk (BEB) method for systems with\noff-diagonal disorder. Using our extended formalism we perform a systematic\nstudy of the effects of non-local disorder-induced correlations and of\noff-diagonal disorder on the density of states and the mobility edge of the\nAnderson localized states. We apply our method to the three-dimensional\nAnderson model with configuration dependent hopping and find fast convergence\nwith modest cluster sizes. Our results are in good agreement with the data\nobtained using exact diagonalization, and the transfer matrix and kernel\npolynomial methods.", "category": "cond-mat_dis-nn" }, { "text": "Coherent Umklapp Scattering of Light from Disordered Photonic Crystals: A theoretical study of the coherent light scattering from disordered photonic\ncrystal is presented. In addition to the conventional enhancement of the\nreflected light intensity into the backscattering direction, the so called\ncoherent backscattering (CBS), the periodic modulation of the dielectric\nfunction in photonic crystals gives rise to a qualitatively new effect:\nenhancement of the reflected light intensity in directions different from the\nbackscattering direction. These additional coherent scattering processes,\ndubbed here {\\em umklapp scattering} (CUS), result in peaks, which are most\npronounced when the incident light beam enters the sample at an angle close to\nthe the Bragg angle. Assuming that the dielectric function modulation is weak,\nwe study the shape of the CUS peaks for different relative lengths of the\nmodulation-induced Bragg attenuation compared to disorder-induced mean free\npath. We show that when the Bragg length increases, then the CBS peak assumes\nits conventional shape, whereas the CUS peak rapidly diminishes in amplitude.\nWe also study the suppression of the CUS peak upon the departure of the\nincident beam from Bragg resonance: we found that the diminishing of the CUS\nintensity is accompanied by substantial broadening. In addition, the peak\nbecomes asymmetric.", "category": "cond-mat_dis-nn" }, { "text": "Multi-overlap simulations of spin glasses: We present results of recent high-statistics Monte Carlo simulations of the\nEdwards-Anderson Ising spin-glass model in three and four dimensions. The study\nis based on a non-Boltzmann sampling technique, the multi-overlap algorithm\nwhich is specifically tailored for sampling rare-event states. We thus\nconcentrate on those properties which are difficult to obtain with standard\ncanonical Boltzmann sampling such as the free-energy barriers F^q_B in the\nprobability density P_J(q) of the Parisi overlap parameter q and the behaviour\nof the tails of the disorder averaged density P(q) = [P_J(q)]_av.", "category": "cond-mat_dis-nn" }, { "text": "Eigenvalue Distribution In The Self-Dual Non-Hermitian Ensemble: We consider an ensemble of self-dual matrices with arbitrary complex entries.\nThis ensemble is closely related to a previously defined ensemble of\nanti-symmetric matrices with arbitrary complex entries. We study the two-level\ncorrelation functions numerically. Although no evidence of non-monotonicity is\nfound in the real space correlation function, a definite shoulder is found. On\nthe analytical side, we discuss the relationship between this ensemble and the\n$\\beta=4$ two-dimensional one-component plasma, and also argue that this\nensemble, combined with other ensembles, exhausts the possible universality\nclasses in non-hermitian random matrix theory. This argument is based on\ncombining the method of hermitization of Feinberg and Zee with Zirnbauer's\nclassification of ensembles in terms of symmetric spaces.", "category": "cond-mat_dis-nn" }, { "text": "Temperature-Dependent Defect Dynamics in the Network Glass SiO2: We investigate the long time dynamics of a strong glass former, SiO2, below\nthe glass transition temperature by averaging single particle trajectories over\ntime windows which comprise roughly 100 particle oscillations. The structure on\nthis coarse-grained time scale is very well defined in terms of coordination\nnumbers, allowing us to identify ill-coordinated atoms, called defects in the\nfollowing. The most numerous defects are OO neighbors, whose lifetimes are\ncomparable to the equilibration time at low temperature. On the other hand SiO\nand OSi defects are very rare and short lived. The lifetime of defects is found\nto be strongly temperature dependent, consistent with activated processes.\nSingle-particle jumps give rise to local structural rearrangements. We show\nthat in SiO2 these structural rearrangements are coupled to the creation or\nannihilation of defects, giving rise to very strong correlations of jumping\natoms and defects.", "category": "cond-mat_dis-nn" }, { "text": "Frustration and sound attenuation in structural glasses: Three classes of harmonic disorder systems (Lennard-Jones like glasses,\npercolators above threshold, and spring disordered lattices) have been\nnumerically investigated in order to clarify the effect of different types of\ndisorder on the mechanism of high frequency sound attenuation. We introduce the\nconcept of frustration in structural glasses as a measure of the internal\nstress, and find a strong correlation between the degree of frustration and the\nexponent alpha that characterizes the momentum dependence of the sound\nattenuation $Gamma(Q)$$\\simeq$$Q^\\alpha$. In particular, alpha decreases from\nabout d+1 in low-frustration systems (where d is the spectral dimension), to\nabout 2 for high frustration systems like the realistic glasses examined.", "category": "cond-mat_dis-nn" }, { "text": "Rotation Diffusion as an Additional Mechanism of Energy Dissipation in\n Polymer Melts: The research is important for a molecular theory of liquid and has a wide\ninterest as an example solving the problem when dynamic parameters of systems\ncan be indirectly connected with their equilibrium properties. In frameworks of\nthe reptation model the power law with the 3.4-exponent for the melt viscosity\nrelation to the molecular weight of linear flexible-chain polymer is predicted\nas distinct from the value 3 expected for a melt of ring macromolecules. To\nfind the exponent close to experimental values it should be taken into account\nthe rotation vibration precession motion of chain ends about the polymer melt\nflow direction.", "category": "cond-mat_dis-nn" }, { "text": "Disorder-Induced Vibrational Localization: The vibrational equivalent of the Anderson tight-binding Hamiltonian has been\nstudied, with particular focus on the properties of the eigenstates at the\ntransition from extended to localized states. The critical energy has been\nfound approximately for several degrees of force-constant disorder using\nsystem-size scaling of the multifractal spectra of the eigenmodes, and the\nspectrum at which there is no system-size dependence has been obtained. This is\nshown to be in good agreement with the critical spectrum for the electronic\nproblem, which has been derived both numerically and by analytic means.\nUniversality of the critical states is therefore suggested also to hold for the\nvibrational problem.", "category": "cond-mat_dis-nn" }, { "text": "Signs of low frequency dispersions in disordered binary dielectric\n mixtures (50-50): Dielectric relaxation in disordered dielectric mixtures are presented by\nemphasizing the interfacial polarization. The obtained results coincide with\nand cause confusion with those of the low frequency dispersion behavior. The\nconsidered systems are composed of two phases on two-dimensional square and\ntriangular topological networks. We use the finite element method to calculate\nthe effective dielectric permittivities of randomly generated structures. The\ndielectric relaxation phenomena together with the dielectric permittivity\nvalues at constant frequencies are investigated, and significant differences of\nthe square and triangular topologies are observed. The frequency dependent\nproperties of some of the generated structures are examined. We conclude that\nthe topological disorder may lead to the normal or anomalous low frequency\ndispersion if the electrical properties of the phases are chosen properly, such\nthat for ``slightly'' {\\em reciprocal mixture}--when $\\sigma_1\\gg\\sigma_2$, and\n$\\epsilon_1<\\epsilon_2$--normal, and while for ``extreme'' {\\em reciprocal\nmixture}--when $\\sigma_1\\gg\\sigma_2$, and $\\epsilon_1\\ll\\epsilon_2$--anomalous\nlow frequency dispersions are obtained. Finally, comparison with experimental\ndata indicates that one can obtain valuable information from simulations when\nthe material properties of the constituents are not available and of\nimportance.", "category": "cond-mat_dis-nn" }, { "text": "Statistics of cycles in large networks: We present a Markov Chain Monte Carlo method for sampling cycle length in\nlarge graphs. Cycles are treated as microstates of a system with many degrees\nof freedom. Cycle length corresponds to energy such that the length histogram\nis obtained as the density of states from Metropolis sampling. In many growing\nnetworks, mean cycle length increases algebraically with system size. The cycle\nexponent $\\alpha$ is characteristic of the local growth rules and not\ndetermined by the degree exponent $\\gamma$. For example, $\\alpha=0.76(4)$ for\nthe Internet at the Autonomous Systems level.", "category": "cond-mat_dis-nn" }, { "text": "Strong Disorder Renewal Approach to DNA denaturation and wetting :\n typical and large deviation properties of the free energy: For the DNA denaturation transition in the presence of random contact\nenergies, or equivalently the disordered wetting transition, we introduce a\nStrong Disorder Renewal Approach to construct the optimal contacts in each\ndisordered sample of size $L$. The transition is found to be of infinite order,\nwith a correlation length diverging with the essential singularity $\\ln \\xi(T)\n\\propto |T-T_c |^{-1}$. In the critical region, we analyze the statistics over\nsamples of the free-energy density $f_L$ and of the contact density, which is\nthe order parameter of the transition. At the critical point, both decay as a\npower-law of the length $L$ but remain distributed, in agreement with the\ngeneral phenomenon of lack of self-averaging at random critical points. We also\nobtain that for any real $q>0$, the moment $\\overline{Z_L^q} $ of order $q$ of\nthe partition function at the critical point is dominated by some exponentially\nrare samples displaying a finite free-energy density, i.e. by the large\ndeviation sector of the probability distribution of the free-energy density.", "category": "cond-mat_dis-nn" }, { "text": "Water adsorption on amorphous silica surfaces: A Car-Parrinello\n simulation study: A combination of classical molecular dynamics (MD) and ab initio\nCar-Parrinello molecular dynamics (CPMD) simulations is used to investigate the\nadsorption of water on a free amorphous silica surface. From the classical MD\nSiO_2 configurations with a free surface are generated which are then used as\nstarting configurations for the CPMD.We study the reaction of a water molecule\nwith a two-membered ring at the temperature T=300K. We show that the result of\nthis reaction is the formation of two silanol groups on the surface. The\nactivation energy of the reaction is estimated and it is shown that the\nreaction is exothermic.", "category": "cond-mat_dis-nn" }, { "text": "Nonlinear transmission and light localization in photonic crystal\n waveguides: We study the light transmission in two-dimensional photonic crystal\nwaveguides with embedded nonlinear defects. First, we derive the effective\ndiscrete equations with long-range interaction for describing the waveguide\nmodes, and demonstrate that they provide a highly accurate generalization of\nthe familiar tight-binding models which are employed, e.g., for the study of\nthe coupled-resonator optical waveguides. Using these equations, we investigate\nthe properties of straight waveguides and waveguide bends with embedded\nnonlinear defects and demonstrate the possibility of the nonlinearity-induced\nbistable transmission. Additionally, we study localized modes in the waveguide\nbends and (linear and nonlinear) transmission of the bent waveguides and\nemphasize the role of evanescent modes in these phenomena.", "category": "cond-mat_dis-nn" }, { "text": "Statistical mechanics of LDPC codes on channels with memory: We present an analytic method of assessing the typical performance of\nlow-density parity-check codes on finite-state Markov channels. We show that\nthis problem is similar to a spin-glass model on a `small-world' lattice. We\napply our methodology to binary-symmetric and binary-asymmetric channels and we\nprovide the critical noise levels for different degrees of channel symmetry.", "category": "cond-mat_dis-nn" }, { "text": "Stark many-body localization: We consider spinless fermions on a finite one-dimensional lattice,\ninteracting via nearest-neighbor repulsion and subject to a strong electric\nfield. In the non-interacting case, due to Wannier-Stark localization, the\nsingle-particle wave functions are exponentially localized even though the\nmodel has no quenched disorder. We show that this system remains localized in\nthe presence of interactions and exhibits physics analogous to models of\nconventional many-body localization (MBL). In particular, the entanglement\nentropy grows logarithmically with time after a quench, albeit with a slightly\ndifferent functional form from the MBL case, and the level statistics of the\nmany-body energy spectrum are Poissonian. We moreover predict that a quench\nexperiment starting from a charge-density wave state would show results similar\nto those of Schreiber et al. [Science 349, 842 (2015)].", "category": "cond-mat_dis-nn" }, { "text": "Experimental test of Sinai's model in DNA unzipping: The experimental measurement of correlation functions and critical exponents\nin disordered systems is key to testing renormalization group (RG) predictions.\nWe mechanically unzip single DNA hairpins with optical tweezers, an\nexperimental realization of the diffusive motion of a particle in a\none-dimensional random force field, known as the Sinai model. We measure the\nunzipping forces $F_w$ as a function of the trap position $w$ in equilibrium\nand calculate the force-force correlator $\\Delta_m(w)$, its amplitude, and\ncorrelation length, finding agreement with theoretical predictions. We study\nthe universal scaling properties since the effective trap stiffness $m^2$\ndecreases upon unzipping. Fluctuations of the position of the base pair at the\nunzipping junction $u$ scales as $u \\sim m^{-\\zeta}$, with a roughness exponent\n$ \\zeta=1.34\\pm0.06$, in agreement with the analytical prediction $\\zeta =\n\\frac{4}{3}$. Our study provides a single-molecule test of the functional RG\napproach for disordered elastic systems in equilibrium.", "category": "cond-mat_dis-nn" }, { "text": "The Gardner transition in physical dimensions: The Gardner transition is the transition that at mean-field level separates a\nstable glass phase from a marginally stable phase. This transition has\nsimilarities with the de Almeida-Thouless transition of spin glasses. We have\nstudied a well-understood problem, that of disks moving in a narrow channel,\nwhich shows many features usually associated with the Gardner transition.\nHowever, we can show that some of these features are artifacts that arise when\na disk escapes its local cage during the quench to higher densities. There is\nevidence that the Gardner transition becomes an avoided transition, in that the\ncorrelation length becomes quite large, of order 15 particle diameters, even in\nour quasi-one-dimensional system.", "category": "cond-mat_dis-nn" }, { "text": "Rayleigh anomalies and disorder-induced mixing of polarizations at\n nanoscale in amorphous solids. Testing 1-octyl-3-methylimidazolium chloride\n glass: Acoustic excitations in topologically disordered media at mesoscale present\nanomalous features with respect to the Debye's theory. In a three-dimensional\nmedium an acoustic excitation is characterized by its phase velocity, intensity\nand polarization. The so-called Rayleigh anomalies, which manifest in\nattenuation and retardation of the acoustic excitations, affect the first two\nproperties. The topological disorder is, however, expected to influence also\nthe third one. Acoustic excitations with a well-defined polarization in the\ncontinuum limit present indeed a so-called mixing of polarizations at\nnanoscale, as attested by experimental observations and Molecular Dynamics\nsimulations. We provide a comprehensive experimental characterization of\nacoustic dynamics properties of a selected glass, 1-octyl-3-methylimidazolium\nchloride glass, whose heterogeneous structure at nanoscale is well-assessed.\nDistinctive features, which can be related to the occurrence of the Rayleigh\nanomalies and of the mixing of polarizations are observed. We develop, in the\nframework of the Random Media Theory, an analytical model that allows a\nquantitative description of all the Rayleigh anomalies and the mixing of\npolarizations. Contrast between theoretical and experimental features for the\nselected glass reveals an excellent agreement. The quantitative theoretical\napproach permits thus to demonstrate how the mixing of polarizations generates\ndistinctive feature in the dynamic structure factor of glasses and to\nunambiguously identify them. The robustness of the proposed theoretical\napproach is validated by its ability to describe as well transverse acoustic\ndynamics.", "category": "cond-mat_dis-nn" }, { "text": "Optimal Vertex Cover for the Small-World Hanoi Networks: The vertex-cover problem on the Hanoi networks HN3 and HN5 is analyzed with\nan exact renormalization group and parallel-tempering Monte Carlo simulations.\nThe grand canonical partition function of the equivalent hard-core repulsive\nlattice-gas problem is recast first as an Ising-like canonical partition\nfunction, which allows for a closed set of renormalization group equations. The\nflow of these equations is analyzed for the limit of infinite chemical\npotential, at which the vertex-cover problem is attained. The relevant fixed\npoint and its neighborhood are analyzed, and non-trivial results are obtained\nboth, for the coverage as well as for the ground state entropy density, which\nindicates the complex structure of the solution space. Using special\nhierarchy-dependent operators in the renormalization group and Monte-Carlo\nsimulations, structural details of optimal configurations are revealed. These\nstudies indicate that the optimal coverages (or packings) are not related by a\nsimple symmetry. Using a clustering analysis of the solutions obtained in the\nMonte Carlo simulations, a complex solution space structure is revealed for\neach system size. Nevertheless, in the thermodynamic limit, the solution\nlandscape is dominated by one huge set of very similar solutions.", "category": "cond-mat_dis-nn" }, { "text": "Record breaking bursts during the compressive failure of porous\n materials: An accurate understanding of the interplay between random and deterministic\nprocesses in generating extreme events is of critical importance in many\nfields, from forecasting extreme meteorological events to the catastrophic\nfailure of materials and in the Earth. Here we investigate the statistics of\nrecord-breaking events in the time series of crackling noise generated by local\nrupture events during the compressive failure of porous materials. The events\nare generated by computer simulations of the uni-axial compression of\ncylindrical samples in a discrete element model of sedimentary rocks that\nclosely resemble those of real experiments. The number of records grows\ninitially as a decelerating power law of the number of events, followed by an\nacceleration immediately prior to failure. We demonstrate the existence of a\ncharacteristic record rank k^* which separates the two regimes of the time\nevolution. Up to this rank deceleration occurs due to the effect of random\ndisorder. Record breaking then accelerates towards macroscopic failure, when\nphysical interactions leading to spatial and temporal correlations dominate the\nlocation and timing of local ruptures. Sub-sequences of bursts between\nconsecutive records are characterized by a power law size distribution with an\nexponent which decreases as failure is approached. High rank records are\npreceded by bursts of increasing size and waiting time between consecutive\nevents and they are followed by a relaxation process. As a reference, surrogate\ntime series are generated by reshuffling the crackling bursts. The record\nstatistics of the uncorrelated surrogates agrees very well with the\ncorresponding predictions of independent identically distributed random\nvariables, which confirms that the temporal and spatial correlation of cracking\nbursts are responsible for the observed unique behaviour.", "category": "cond-mat_dis-nn" }, { "text": "Non equilibrium dynamics below the super-roughening transition: The non equilibrium relaxational dynamics of the solid on solid model on a\ndisordered substrate and the Sine Gordon model with random phase shifts is\nstudied numerically. Close to the super-roughening temperature $T_g$ our\nresults for the autocorrelations, spatial correlations and response function as\nwell as for the fluctuation dissipation ratio (FDR) agree well with the\nprediction of a recent one loop RG calculation, whereas deep in the glassy low\ntemperature phase substantial deviations occur. The change in the low\ntemperature behavior of these quantities compared with the RG predictions is\nshown to be contained in a change of the functional temperature dependence of\nthe dynamical exponent $z(T)$, which relates the age $t$ of the system with a\nlength scale ${\\cal L}(t)$: $z(T)$ changes from a linear $T$-dependence close\nto $T_g$ to a 1/T-behavior far away from $T_g$. By identifying spatial domains\nas connected patches of the exactly computable ground states of the system we\ndemonstrate that the growing length scale ${\\cal L}(t)$ is the characteristic\nsize of thermally fluctuating clusters around ``typical'' long-lived\nconfigurations.", "category": "cond-mat_dis-nn" }, { "text": "Non-Abelian chiral symmetry controls random scattering in two-band\n models: We study the dynamics of non-interacting quantum particles with two bands in\nthe presence of random scattering. The two bands are associated with a chiral\nsymmetry. After breaking the latter by a potential, we still find that the\nquantum dynamics is controlled by a non-Abelian chiral symmetry. The\npossibility of spontaneous symmetry breaking is analyzed within a\nself-consistent approach, and the instability of a symmetric solution is\ndiscussed.", "category": "cond-mat_dis-nn" }, { "text": "Fluctuation effects in metapopulation models: percolation and pandemic\n threshold: Metapopulation models provide the theoretical framework for describing\ndisease spread between different populations connected by a network. In\nparticular, these models are at the basis of most simulations of pandemic\nspread. They are usually studied at the mean-field level by neglecting\nfluctuations. Here we include fluctuations in the models by adopting fully\nstochastic descriptions of the corresponding processes. This level of\ndescription allows to address analytically, in the SIS and SIR cases, problems\nsuch as the existence and the calculation of an effective threshold for the\nspread of a disease at a global level. We show that the possibility of the\nspread at the global level is described in terms of (bond) percolation on the\nnetwork. This mapping enables us to give an estimate (lower bound) for the\npandemic threshold in the SIR case for all values of the model parameters and\nfor all possible networks.", "category": "cond-mat_dis-nn" }, { "text": "Memory effects, two color percolation, and the temperature dependence of\n Mott's variable range hopping: There are three basic processes that determine hopping transport: (a) hopping\nbetween normally empty sites (i.e. having exponentially small occupation\nnumbers at equilibrium); (b) hopping between normally occupied sites, and (c)\ntransitions between normally occupied and unoccupied sites. In conventional\ntheories all these processes are considered Markovian and the correlations of\noccupation numbers of different sites are believed to be small(i.e. not\nexponential in temperature). We show that, contrary to this belief, memory\neffects suppress the processes of type (c), and manifest themselves in a\nsubleading {\\em exponential} temperature dependence of the variable range\nhopping conductivity. This temperature dependence originates from the property\nthat sites of type (a) and (b) form two independent resistor networks that are\nweakly coupled to each other by processes of type (c). This leads to a\ntwo-color percolation problem which we solve in the critical region.", "category": "cond-mat_dis-nn" }, { "text": "Molecular dynamics simulation of the fragile glass former\n ortho-terphenyl: a flexible molecule model: We present a realistic model of the fragile glass former orthoterphenyl and\nthe results of extensive molecular dynamics simulations in which we\ninvestigated its basic static and dynamic properties. In this model the\ninternal molecular interactions between the three rigid phenyl rings are\ndescribed by a set of force constants, including harmonic and anharmonic terms;\nthe interactions among different molecules are described by Lennard-Jones\nsite-site potentials. Self-diffusion properties are discussed in detail\ntogether with the temperature and momentum dependencies of the\nself-intermediate scattering function. The simulation data are compared with\nexisting experimental results and with the main predictions of the Mode\nCoupling Theory.", "category": "cond-mat_dis-nn" }, { "text": "Percolation Thresholds of the Fortuin-Kasteleyn Cluster for a Potts\n Gauge Glass Model on Complex Networks: Analytical Results on the Nishimori\n Line: It was pointed out by de Arcangelis et al. [Europhys. Lett. 14 (1991), 515]\nthat the correct understanding of the percolation phenomenon of the\nFortuin-Kasteleyn cluster in the Edwards-Anderson model is important since a\ndynamical transition, which is characterized by a parameter called the Hamming\ndistance or damage, and the percolation transition are related to a transition\nfor a signal propagating between spins. We show analytically the percolation\nthresholds of the Fortuin-Kasteleyn cluster for a Potts gauge glass model,\nwhich is an extended model of the Edwards-Anderson model, on random graphs with\narbitary degree distributions. The results are shown on the Nishimori line. We\nalso show the results for the infinite-range model.", "category": "cond-mat_dis-nn" }, { "text": "d=3 random field behavior near percolation: The highly diluted antiferromagnet Mn(0.35)Zn(0.65)F2 has been investigated\nby neutron scattering for H>0. A low-temperature (T<11K), low-field (H<1T)\npseudophase transition boundary separates a partially antiferromagnetically\nordered phase from the paramagnetic one. For 1 of the initial network is\nabove, equal to, or below the threshold _c corresponding to the emergence of\nthe giant k-core. We find that above the threshold the network relaxes\nexponentially to the k-core. The system manifests the phenomenon known as\n\"critical slowing down\", as the relaxation time diverges when tends to\n_c. At the threshold, the dynamics become critical characterized by a\npower-law relaxation (1/t^2). Below the threshold, a long-lasting transient\nprocess (a \"plateau\" stage) occurs. This transient process ends with a collapse\nin which the entire network disappears completely. The duration of the process\ndiverges when tends to _c. We show that the critical dynamics of the\npruning are determined by branching processes of spreading damage. Clusters of\nnodes of degree exactly k are the evolving substrate for these branching\nprocesses. Our theory completely describes this branching cascade of damage in\nuncorrelated networks by providing the time dependent distribution function of\nbranching. These theoretical results are supported by our simulations of the\n$k$-core pruning in Erdos-Renyi graphs.", "category": "cond-mat_dis-nn" }, { "text": "New class of level statistics in correlated disordered chains: We study the properties of the level statistics of 1D disordered systems with\nlong-range spatial correlations. We find a threshold value in the degree of\ncorrelations below which in the limit of large system size the level statistics\nfollows a Poisson distribution (as expected for 1D uncorrelated disordered\nsystems), and above which the level statistics is described by a new class of\ndistribution functions. At the threshold, we find that with increasing system\nsize the standard deviation of the function describing the level statistics\nconverges to the standard deviation of the Poissonian distribution as a power\nlaw. Above the threshold we find that the level statistics is characterized by\ndifferent functional forms for different degrees of correlations.", "category": "cond-mat_dis-nn" }, { "text": "Universal correlations between shocks in the ground state of elastic\n interfaces in disordered media: The ground state of an elastic interface in a disordered medium undergoes\ncollective jumps upon variation of external parameters. These mesoscopic jumps\nare called shocks, or static avalanches. Submitting the interface to a\nparabolic potential centered at $w$, we study the avalanches which occur as $w$\nis varied. We are interested in the correlations between the avalanche sizes\n$S_1$ and $S_2$ occurring at positions $w_1$ and $w_2$. Using the Functional\nRenormalization Group (FRG), we show that correlations exist for realistic\ninterface models below their upper critical dimension. Notably, the connected\nmoment $ \\langle S_1 S_2 \\rangle^c$ is up to a prefactor exactly the\nrenormalized disorder correlator, itself a function of $|w_2-w_1|$. The latter\nis the universal function at the center of the FRG; hence correlations between\nshocks are universal as well. All moments and the full joint probability\ndistribution are computed to first non-trivial order in an $\\epsilon$-expansion\nbelow the upper critical dimension. To quantify the local nature of the\ncoupling between avalanches, we calculate the correlations of their local\njumps. We finally test our predictions against simulations of a particle in\nrandom-bond and random-force disorder, with surprisingly good agreement.", "category": "cond-mat_dis-nn" }, { "text": "Derivatives and inequalities for order parameters in the Ising spin\n glass: Identities and inequalities are proved for the order parameters, correlation\nfunctions and their derivatives of the Ising spin glass. The results serve as\nadditional evidence that the ferromagnetic phase is composed of two regions,\none with strong ferromagnetic ordering and the other with the effects of\ndisorder dominant. The Nishimori line marks a crossover between these two\nregions.", "category": "cond-mat_dis-nn" }, { "text": "Metastable states in disordered Ising magnets in mean-field\n approximation: The mechanism of appearance of exponentially large number of metastable\nstates in magnetic phases of disordered Ising magnets with short-range random\nexchange is suggested. It is based on the assumption that transitions into\ninhomogeneous magnetic phases results from the condensation of macroscopically\nlarge number of sparse delocalized modes near the localization threshold. The\nproperties of metastable states in random magnets with zero ground state\nmagnetization (dilute antiferromagnet, binary spin glass, dilute ferromagnet\nwith dipole interaction) has been obtained in framework of this mechanism using\nvariant of mean-field approximation. The relations between the characteristics\nof slow nonequilibrium processes in magnetic phases and thermodynamic\nparameters of metastable states are established.", "category": "cond-mat_dis-nn" }, { "text": "Spreading in Disordered Lattices with Different Nonlinearities: We study the spreading of initially localized states in a nonlinear\ndisordered lattice described by the nonlinear Schr\\\"odinger equation with\nrandom on-site potentials - a nonlinear generalization of the Anderson model of\nlocalization. We use a nonlinear diffusion equation to describe the\nsubdiffusive spreading. To confirm the self-similar nature of the evolution we\ncharacterize the peak structure of the spreading states with help of R\\'enyi\nentropies and in particular with the structural entropy. The latter is shown to\nremain constant over a wide range of time. Furthermore, we report on the\ndependence of the spreading exponents on the nonlinearity index in the\ngeneralized nonlinear Schr\\\"odinger disordered lattice, and show that these\nquantities are in accordance with previous theoretical estimates, based on\nassumptions of weak and very weak chaoticity of the dynamics.", "category": "cond-mat_dis-nn" }, { "text": "Percolation Transition in a Topological Phase: Transition out of a topological phase is typically characterized by\ndiscontinuous changes in topological invariants along with bulk gap closings.\nHowever, as a clean system is geometrically punctured, it is natural to ask the\nfate of an underlying topological phase. To understand this physics we\nintroduce and study both short and long-ranged toy models where a one\ndimensional topological phase is subjected to bond percolation protocols. We\nfind that non-trivial boundary phenomena follow competing energy scales even\nwhile global topological response is governed via geometrical properties of the\npercolated lattice. Using numerical, analytical and appropriate mean-field\nstudies we uncover the rich phenomenology and the various cross-over regimes of\nthese systems. In particular, we discuss emergence of \"fractured topological\nregion\" where an overall trivial system contains macroscopic number of\ntopological clusters. Our study shows the interesting physics that can arise\nfrom an interplay of geometrical disorder within a topological phase.", "category": "cond-mat_dis-nn" }, { "text": "The dipolar spin glass transition in three dimensions: Dilute dipolar Ising magnets remain a notoriously hard problem to tackle both\nanalytically and numerically because of long-ranged interactions between spins\nas well as rare region effects. We study a new type of anisotropic dilute\ndipolar Ising system in three dimensions [Phys. Rev. Lett. {\\bf 114}, 247207\n(2015)] that arises as an effective description of randomly diluted classical\nspin ice, a prototypical spin liquid in the disorder-free limit, with a small\nfraction $x$ of non-magnetic impurities. Metropolis algorithm within a parallel\nthermal tempering scheme fails to achieve equilibration for this problem\nalready for small system sizes. Motivated by previous work [Phys. Rev. X {\\bf\n4}, 041016 (2014)] on uniaxial random dipoles, we present an improved cluster\nMonte Carlo algorithm that is tailor-made for removing the equilibration\nbottlenecks created by clusters of {\\it effectively frozen} spins. By\nperforming large-scale simulations down to $x=1/128$ and using finite size\nscaling, we show the existence of a finite-temperature spin glass transition\nand give strong evidence that the universality of the critical point is\nindependent of $x$ when it is small. In this $x \\ll 1$ limit, we also provide a\nfirst estimate of both the thermal exponent, $\\nu=1.27(8)$, and the anomalous\nexponent, $\\eta=0.228(35)$.", "category": "cond-mat_dis-nn" }, { "text": "Anderson localization of emergent quasiparticles: Spinon and vison\n interplay at finite temperature in a $\\mathbb{Z}_2$ gauge theory in three\n dimensions: Fractional statistics of quasiparticle excitations often plays an important\nrole in the detection and characterization of topological systems. In this\npaper, we investigate the case of a three-dimensional (3D) Z2 gauge theory,\nwhere the excitations take the form of bosonic spinon quasiparticle and vison\nflux tubes, with mutual semionic statistics. We focus on an experimentally\nrelevant intermediate temperature regime, where sparse spinons hop coherently\non a dense quasistatic and stochastic vison background. The effective\nHamiltonian reduces to a random-sign bimodal tight-binding model, where both\nthe particles and the disorder are borne out of the same underlying quantum\nspin liquid (QSL) degrees of freedom, and the coupling between the two is\npurely driven by the mutual fractional statistics. We study the localization\nproperties and observe a mobility edge located close to the band edge, whose\ntransition belongs to the 3D Anderson model universality class. Spinons allowed\nto propagate through the quasistatic vison background appear to display quantum\ndiffusive behavior. When the visons are allowed to relax, in response to the\npresence of spinons in equilibrium, we observe the formation of vison depletion\nregions slave to the support of the spinon wavefunction. We discuss how this\nbehavior can give rise to measurable effects in the relaxation, response and\ntransport properties of the system and how these may be used as signatures of\nthe mutual semionic statistics and as precursors of the QSL phase arising in\nthe system at lower temperatures.", "category": "cond-mat_dis-nn" }, { "text": "Enhancing the spectral gap of networks by node removal: Dynamics on networks are often characterized by the second smallest\neigenvalue of the Laplacian matrix of the network, which is called the spectral\ngap. Examples include the threshold coupling strength for synchronization and\nthe relaxation time of a random walk. A large spectral gap is usually\nassociated with high network performance, such as facilitated synchronization\nand rapid convergence. In this study, we seek to enhance the spectral gap of\nundirected and unweighted networks by removing nodes because, practically, the\nremoval of nodes often costs less than the addition of nodes, addition of\nlinks, and rewiring of links. In particular, we develop a perturbative method\nto achieve this goal. The proposed method realizes better performance than\nother heuristic methods on various model and real networks. The spectral gap\nincreases as we remove up to half the nodes in most of these networks.", "category": "cond-mat_dis-nn" }, { "text": "Localization Transition in Incommensurate non-Hermitian Systems: A class of one-dimensional lattice models with incommensurate complex\npotential $V(\\theta)=2[\\lambda_r cos(\\theta)+i \\lambda_i sin(\\theta)]$ is found\nto exhibit localization transition at $|\\lambda_r|+|\\lambda_i|=1$. This\ntransition from extended to localized states manifests in the behavior of the\ncomplex eigenspectum. In the extended phase, states with real eigenenergies\nhave finite measure and this measure goes to zero in the localized phase.\nFurthermore, all extended states exhibit real spectrum provided $|\\lambda_r|\n\\ge |\\lambda_i|$. Another novel feature of the system is the fact that the\nimaginary part of the spectrum is sensitive to the boundary conditions {\\it\nonly at the onset to localization}.", "category": "cond-mat_dis-nn" }, { "text": "Mean field theory for the three-dimensional Coulomb glass: We study the low temperature phase of the 3D Coulomb glass within a mean\nfield approach which reduces the full problem to an effective single site model\nwith a non-trivial replica structure. We predict a finite glass transition\ntemperature $T_c$, and a glassy low temperature phase characterized by\npermanent criticality. The latter is shown to assure the saturation of the\nEfros-Shklovskii Coulomb gap in the density of states. We find this pseudogap\nto be universal due to a fixed point in Parisi's flow equations. The latter is\ngiven a physical interpretation in terms of a dynamical self-similarity of the\nsystem in the long time limit, shedding new light on the concept of effective\ntemperature. From the low temperature solution we infer properties of the\nhierarchical energy landscape, which we use to make predictions about the\nmaster function governing the aging in relaxation experiments.", "category": "cond-mat_dis-nn" }, { "text": "Finite size scaling in neural networks: We demonstrate that the fraction of pattern sets that can be stored in\nsingle- and hidden-layer perceptrons exhibits finite size scaling. This feature\nallows to estimate the critical storage capacity \\alpha_c from simulations of\nrelatively small systems. We illustrate this approach by determining \\alpha_c,\ntogether with the finite size scaling exponent \\nu, for storing Gaussian\npatterns in committee and parity machines with binary couplings and up to K=5\nhidden units.", "category": "cond-mat_dis-nn" }, { "text": "Phase transitions in diluted negative-weight percolation models: We investigate the geometric properties of loops on two-dimensional lattice\ngraphs, where edge weights are drawn from a distribution that allows for\npositive and negative weights. We are interested in the appearance of spanning\nloops of total negative weight. The resulting percolation problem is\nfundamentally different from conventional percolation, as we have seen in a\nprevious study of this model for the undiluted case.\n Here, we investigate how the percolation transition is affected by additional\ndilution. We consider two types of dilution: either a certain fraction of edges\nexhibit zero weight, or a fraction of edges is even absent. We study these\nsystems numerically using exact combinatorial optimization techniques based on\nsuitable transformations of the graphs and applying matching algorithms. We\nperform a finite-size scaling analysis to obtain the phase diagram and\ndetermine the critical properties of the phase boundary.\n We find that the first type of dilution does not change the universality\nclass compared to the undiluted case whereas the second type of dilution leads\nto a change of the universality class.", "category": "cond-mat_dis-nn" }, { "text": "Influence of disorder on a Bragg microcavity: Using the resonant-state expansion for leaky optical modes of a planar Bragg\nmicrocavity, we investigate the influence of disorder on its fundamental cavity\nmode. We model the disorder by randomly varying the thickness of the Bragg-pair\nslabs (composing the mirrors) and the cavity, and calculate the resonant energy\nand linewidth of each disordered microcavity exactly, comparing the results\nwith the resonant-state expansion for a large basis set and within its first\nand second orders of perturbation theory. We show that random shifts of\ninterfaces cause a growth of the inhomogeneous broadening of the fundamental\nmode that is proportional to the magnitude of disorder. Simultaneously, the\nquality factor of the microcavity decreases inversely proportional to the\nsquare of the magnitude of disorder. We also find that first-order perturbation\ntheory works very accurately up to a reasonably large disorder magnitude,\nespecially for calculating the resonance energy, which allows us to derive\nqualitatively the scaling of the microcavity properties with disorder strength.", "category": "cond-mat_dis-nn" }, { "text": "Self-organized criticality in neural network models: It has long been argued that neural networks have to establish and maintain a\ncertain intermediate level of activity in order to keep away from the regimes\nof chaos and silence. Strong evidence for criticality has been observed in\nterms of spatio-temporal activity avalanches first in cultures of rat cortex by\nBeggs and Plenz (2003) and subsequently in many more experimental setups. These\nfindings sparked intense research on theoretical models for criticality and\navalanche dynamics in neural networks, where usually some dynamical order\nparameter is fed back onto the network topology by adapting the synaptic\ncouplings. We here give an overview of existing theoretical models of dynamical\nnetworks. While most models emphasize biological and neurophysiological detail,\nour path here is different: we pick up the thread of an early self-organized\ncritical neural network model by Bornholdt and Roehl (2001) and test its\napplicability in the light of experimental data. Keeping the simplicity of\nearly models, and at the same time lifting the drawback of a spin formulation\nwith respect to the biological system, we here study an improved model\n(Rybarsch and Bornholdt, 2012b) and show that it adapts to criticality\nexhibiting avalanche statistics that compare well with experimental data\nwithout the need for parameter tuning.", "category": "cond-mat_dis-nn" }, { "text": "Avalanches and perturbation theory in the random-field Ising model: Perturbation theory for the random-field Ising model (RFIM) has the infamous\nattribute that it predicts at all orders a dimensional-reduction property for\nthe critical behavior that turns out to be wrong in low dimension. Guided by\nour previous work based on the nonperturbative functional renormalization group\n(NP-FRG), we show that one can still make some use of the perturbation theory\nfor a finite range of dimension below the upper critical dimension, d=6. The\nnew twist is to account for the influence of large-scale zero-temperature\nevents known as avalanches. These avalanches induce nonanalyticities in the\nfield dependence of the correlation functions and renormalized vertices, and we\ncompute in a loop expansion the eigenvalue associated with the corresponding\nanomalous operator. The outcome confirms the NP-FRG prediction that the\ndimensional-reduction fixed point correctly describes the dominant critical\nscaling of the RFIM above some dimension close to 5 but not below.", "category": "cond-mat_dis-nn" }, { "text": "Spectral properties of complex networks: This review presents an account of the major works done on spectra of\nadjacency matrices drawn on networks and the basic understanding attained so\nfar. We have divided the review under three sections: (a) extremal eigenvalues,\n(b) bulk part of the spectrum and (c) degenerate eigenvalues, based on the\nintrinsic properties of eigenvalues and the phenomena they capture. We have\nreviewed the works done for spectra of various popular model networks, such as\nthe Erd\\H{o}s-R\\'enyi random networks, scale-free networks, 1-d lattice,\nsmall-world networks, and various different real-world networks. Additionally,\npotential applications of spectral properties for natural processes have been\nreviewed.", "category": "cond-mat_dis-nn" }, { "text": "Erratum: Small-world networks: Evidence for a crossover picture: We correct the value of the exponent \\tau.", "category": "cond-mat_dis-nn" }, { "text": "Onset of reptations and critical hysteretic behavior in disordered\n systems: Zero-temperature random coercivity Ising model with antiferromagnetic-like\ninteractions is used to study closure of minor hysteresis loops and wiping-out\nproperty (Return Point Memory) in hysteretic behavior. Numerical simulations in\ntwo dimensions as well as mean-field modeling show a critical phenomenon in the\nhysteretic behavior associated with the loss of minor loop closure and the\nonset of reptations. Power law scaling of the extent of minor loop reptations\nis observed.", "category": "cond-mat_dis-nn" }, { "text": "The September 11 Attack: A Percolation of Individual Passive Support: A model for terrorism is presented using the theory of percolation. Terrorism\npower is related to the spontaneous formation of random backbones of people who\nare sympathetic to terrorism but without being directly involved in it. They\njust don't oppose in case they could. In the past such friendly-to-terrorism\nbackbones have been always existing but were of finite size and localized to a\ngiven geographical area. The September 11 terrorist attack on the US has\nrevealed for the first time the existence of a world wide spread extension. It\nis argued to have result from a sudden world percolation of otherwise\nunconnected and dormant world spread backbones of passive supporters. The\nassociated strategic question is then to determine if collecting ground\ninformation could have predict and thus avoid such a transition. Our results\nshow the answer is no, voiding the major criticism against intelligence\nservices. To conclude the impact of military action is discussed.", "category": "cond-mat_dis-nn" }, { "text": "A tomography of the GREM: beyond the REM conjecture: Recently, Bauke and Mertens conjectured that the local statistics of energies\nin random spin systems with discrete spin space should in most circumstances be\nthe same as in the random energy model. This was proven in a large class of\nmodels for energies that do not grow too fast with the system size. Considering\nthe example of the generalized random energy model, we show that the conjecture\nbreaks down for energies proportional to the volume of the system, and describe\nthe far more complex behavior that then sets in.", "category": "cond-mat_dis-nn" }, { "text": "Renormalization for Discrete Optimization: The renormalization group has proven to be a very powerful tool in physics\nfor treating systems with many length scales. Here we show how it can be\nadapted to provide a new class of algorithms for discrete optimization. The\nheart of our method uses renormalization and recursion, and these processes are\nembedded in a genetic algorithm. The system is self-consistently optimized on\nall scales, leading to a high probability of finding the ground state\nconfiguration. To demonstrate the generality of such an approach, we perform\ntests on traveling salesman and spin glass problems. The results show that our\n``genetic renormalization algorithm'' is extremely powerful.", "category": "cond-mat_dis-nn" }, { "text": "Interference phenomena in radiation of a charged particle moving in a\n system with one-dimensional randomness: The contribution of interference effects to the radiation of a charged\nparticle moving in a medium of randomly spaced plates is considered. In the\nangular dependent radiation intensity a peak appears at angles\n$\\theta\\sim\\pi-\\gamma^{-1}$, where $\\gamma$ is the Lorentz factor of the\ncharged particle.", "category": "cond-mat_dis-nn" }, { "text": "On the Paramagnetic Impurity Concentration of Silicate Glasses from\n Low-Temperature Physics: The concentration of paramagnetic trace impurities in glasses can be\ndetermined via precise SQUID measurements of the sample's magnetization in a\nmagnetic field. However the existence of quasi-ordered structural\ninhomogeneities in the disordered solid causes correlated tunneling currents\nthat can contribute to the magnetization, surprisingly, also at the higher\ntemperatures. We show that taking into account such tunneling systems gives\nrise to a good agreement between the concentrations extracted from SQUID\nmagnetization and those extracted from low-temperature heat capacity\nmeasurements. Without suitable inclusion of such magnetization contribution\nfrom the tunneling currents we find that the concentration of paramagnetic\nimpurities gets considerably over-estimated. This analysis represents a further\npositive test for the structural inhomogeneity theory of the magnetic effects\nin the cold glasses.", "category": "cond-mat_dis-nn" }, { "text": "Universality class of 3D site-diluted and bond-diluted Ising systems: We present a finite-size scaling analysis of high-statistics Monte Carlo\nsimulations of the three-dimensional randomly site-diluted and bond-diluted\nIsing model. The critical behavior of these systems is affected by\nslowly-decaying scaling corrections which make the accurate determination of\ntheir universal asymptotic behavior quite hard, requiring an effective control\nof the scaling corrections. For this purpose we exploit improved Hamiltonians,\nfor which the leading scaling corrections are suppressed for any thermodynamic\nquantity, and improved observables, for which the leading scaling corrections\nare suppressed for any model belonging to the same universality class.\n The results of the finite-size scaling analysis provide strong numerical\nevidence that phase transitions in three-dimensional randomly site-diluted and\nbond-diluted Ising models belong to the same randomly dilute Ising universality\nclass. We obtain accurate estimates of the critical exponents, $\\nu=0.683(2)$,\n$\\eta=0.036(1)$, $\\alpha=-0.049(6)$, $\\gamma=1.341(4)$, $\\beta=0.354(1)$,\n$\\delta=4.792(6)$, and of the leading and next-to-leading correction-to-scaling\nexponents, $\\omega=0.33(3)$ and $\\omega_2=0.82(8)$.", "category": "cond-mat_dis-nn" }, { "text": "Comment on \"Quantum and Classical Glass Transitions in\n LiHo$_{x}$Y$_{1-x}$F$_4$\" by C. Ancona-Torres, D.M. Silevitch, G. Aeppli, and\n T. F. Rosenbaum, Phys. Rev. Lett. 101, 057201 (2008): We show in this comment that the claim by Ancona-Torres et al. of an\nequilibrium quantum or classical phase transition in the LiHo$_x$Y$_{1-x}$F$_4$\nsystem is not supported by a rigorous scaling analysis.", "category": "cond-mat_dis-nn" }, { "text": "Beyond universal behavior in the one-dimensional chain with random\n nearest neighbor hopping: We study the one-dimensional nearest neighbor tight binding model of\nelectrons with independently distributed random hopping and no on-site\npotential (i.e. off-diagonal disorder with particle-hole symmetry, leading to\nsub-lattice symmetry, for each realization). For non-singular distributions of\nthe hopping, it is known that the model exhibits a universal, singular behavior\nof the density of states $\\rho(E) \\sim 1/|E \\ln^3|E||$ and of the localization\nlength $\\xi(E) \\sim |\\ln|E||$, near the band center $E = 0$. (This singular\nbehavior is also applicable to random XY and Heisenberg spin chains; it was\nfirst obtained by Dyson for a specific random harmonic oscillator chain).\nSimultaneously, the state at $E = 0$ shows a universal, sub-exponential decay\nat large distances $\\sim \\exp [ -\\sqrt{r/r_0} ]$. In this study, we consider\nsingular, but normalizable, distributions of hopping, whose behavior at small\n$t$ is of the form $\\sim 1/ [t \\ln^{\\lambda+1}(1/t) ]$, characterized by a\nsingle, continuously tunable parameter $\\lambda > 0$. We find, using a\ncombination of analytic and numerical methods, that while the universal result\napplies for $\\lambda > 2$, it no longer holds in the interval $0 < \\lambda <\n2$. In particular, we find that the form of the density of states singularity\nis enhanced (relative to the Dyson result) in a continuous manner depending on\nthe non-universal parameter $\\lambda$; simultaneously, the localization length\nshows a less divergent form at low energies, and ceases to diverge below\n$\\lambda = 1$. For $\\lambda < 2$, the fall-off of the $E = 0$ state at large\ndistances also deviates from the universal result, and is of the form $\\sim\n\\exp [-(r/r_0)^{1/\\lambda}]$, which decays faster than an exponential for\n$\\lambda < 1$.", "category": "cond-mat_dis-nn" }, { "text": "Super-diffusion in optical realizations of Anderson localization: We discuss the dynamics of particles in one dimension in potentials that are\nrandom both in space and in time. The results are applied to recent optics\nexperiments on Anderson localization, in which the transverse spreading of a\nbeam is suppressed by random fluctuations in the refractive index. If the\nrefractive index fluctuates along the direction of the paraxial propagation of\nthe beam, the localization is destroyed. We analyze this broken localization,\nin terms of the spectral decomposition of the potential. When the potential has\na discrete spectrum, the spread is controlled by the overlap of Chirikov\nresonances in phase space. As the number of Fourier components is increased,\nthe resonances merge into a continuum, which is described by a Fokker-Planck\nequation. We express the diffusion coefficient in terms of the spectral\nintensity of the potential. For a general class of potentials that are commonly\nused in optics, the solutions of the Fokker-Planck equation exhibit anomalous\ndiffusion in phase space, implying that when Anderson localization is broken by\ntemporal fluctuations of the potential, the result is transport at a rate\nsimilar to a ballistic one or even faster. For a class of potentials which\narise in some existing realizations of Anderson localization atypical behavior\nis found.", "category": "cond-mat_dis-nn" }, { "text": "AC-field-controlled localization-delocalization transition in one\n dimensional disordered system: Based on the random dimer model, we study correlated disorder in a one\ndimensional system driven by a strong AC field. As the correlations in a random\nsystem may generate extended states and enhance transport in DC fields, we\nexplore the role that AC fields have on these properties. We find that similar\nto ordered structures, AC fields renormalize the effective hopping constant to\na smaller value, and thus help to localize a state. We find that AC fields\ncontrol then a localization-delocalization transition in a given one\ndimensional systems with correlated disorder. The competition between band\nrenormalization (band collapse/dynamic localization), Anderson localization,\nand the structure correlation is shown to result in interesting transport\nproperties.", "category": "cond-mat_dis-nn" }, { "text": "Minimum spanning trees on weighted scale-free networks: A complete understanding of real networks requires us to understand the\nconsequences of the uneven interaction strengths between a system's components.\nHere we use the minimum spanning tree (MST) to explore the effect of weight\nassignment and network topology on the organization of complex networks. We\nfind that if the weight distribution is correlated with the network topology,\nthe MSTs are either scale-free or exponential. In contrast, when the\ncorrelations between weights and topology are absent, the MST degree\ndistribution is a power-law and independent of the weight distribution. These\nresults offer a systematic way to explore the impact of weak links on the\nstructure and integrity of complex networks.", "category": "cond-mat_dis-nn" }, { "text": "Calorimetric glass transition in a mean field theory approach: The study of the properties of glass-forming liquids is difficult for many\nreasons. Analytic solutions of mean field models are usually available only for\nsystems embedded in a space with an unphysically high number of spatial\ndimensions; on the experimental and numerical side, the study of the properties\nof metastable glassy states requires to thermalize the system in the\nsupercooled liquid phase, where the thermalization time may be extremely large.\nWe consider here an hard-sphere mean field model which is solvable in any\nnumber of spatial dimensions; moreover we easily obtain thermalized\nconfigurations even in the glass phase. We study the three dimensional version\nof this model and we perform Monte Carlo simulations which mimic heating and\ncooling experiments performed on ultra-stable glasses. The numerical findings\nare in good agreement with the analytical results and qualitatively capture the\nfeatures of ultra-stable glasses observed in experiments.", "category": "cond-mat_dis-nn" }, { "text": "Second order phase transition in the six-dimensional Ising spin glass on\n a field: The very existence of a phase transition for spin glasses in an external\nmagnetic field is controversial, even in high dimensions. We carry out massive\nsimulations of the Ising spin-glass in a field, in six dimensions (which,\naccording to classical, but not generally accepted, field-theoretical studies,\nis the upper critical dimension). We find a phase transition and compute the\ncritical exponents, that are found to be compatible with their mean-field\nvalues. We also find that the replica-symmetric Hamiltonian describes the\nscaling of the renormalized couplings near the phase transition.", "category": "cond-mat_dis-nn" }, { "text": "Slow and Long-ranged Dynamical Heterogeneities in Dissipative Fluids: A two-dimensional bidisperse granular fluid is shown to exhibit pronounced\nlong-ranged dynamical heterogeneities as dynamical arrest is approached. Here\nwe focus on the most direct approach to study these heterogeneities: we\nidentify clusters of slow particles and determine their size, $N_c$, and their\nradius of gyration, $R_G$. We show that $N_c\\propto R_G^{d_f}$, providing\ndirect evidence that the most immobile particles arrange in fractal objects\nwith a fractal dimension, $d_f$, that is observed to increase with packing\nfraction $\\phi$. The cluster size distribution obeys scaling, approaching an\nalgebraic decay in the limit of structural arrest, i.e., $\\phi\\to\\phi_c$.\nAlternatively, dynamical heterogeneities are analyzed via the four-point\nstructure factor $S_4(q,t)$ and the dynamical susceptibility $\\chi_4(t)$.\n$S_4(q,t)$ is shown to obey scaling in the full range of packing fractions,\n$0.6\\leq\\phi\\leq 0.805$, and to become increasingly long-ranged as\n$\\phi\\to\\phi_c$. Finite size scaling of $\\chi_4(t)$ provides a consistency\ncheck for the previously analyzed divergences of $\\chi_4(t)\\propto\n(\\phi-\\phi_c)^{-\\gamma_{\\chi}}$ and the correlation length $\\xi\\propto\n(\\phi-\\phi_c)^{-\\gamma_{\\xi}}$. We check the robustness of our results with\nrespect to our definition of mobility. The divergences and the scaling for\n$\\phi\\to\\phi_c$ suggest a non-equilibrium glass transition which seems\nqualitatively independent of the coefficient of restitution.", "category": "cond-mat_dis-nn" }, { "text": "Entanglement entropy of random partitioning: We study the entanglement entropy of random partitions in one- and\ntwo-dimensional critical fermionic systems. In an infinite system we consider a\nfinite, connected (hypercubic) domain of linear extent $L$, the points of which\nwith probability $p$ belong to the subsystem. The leading contribution to the\naverage entanglement entropy is found to scale with the volume as $a(p) L^D$,\nwhere $a(p)$ is a non-universal function, to which there is a logarithmic\ncorrection term, $b(p)L^{D-1}\\ln L$. In $1D$ the prefactor is given by\n$b(p)=\\frac{c}{3} f(p)$, where $c$ is the central charge of the model and\n$f(p)$ is a universal function. In $2D$ the prefactor has a different\nfunctional form of $p$ below and above the percolation threshold.", "category": "cond-mat_dis-nn" }, { "text": "Short-range Magnetic interactions in the Spin-Ice compound\n Ho$_{2}$Ti$_{2}$O$_{7}$: Magnetization and susceptibility studies on single crystals of the pyrochlore\nHo$_{2}$Ti$_{2}$O$_{7}$ are reported for the first time. Magnetization\nisotherms are shown to be qualitatively similar to that predicted by the\nnearest neighbor spin-ice model. Below the lock-in temperature, $T^{\\ast\n}\\simeq 1.97$ K, magnetization is consistent with the locking of spins along\n[111] directions in a specific two-spins-in, two-spins-out arrangement. Below\n$T^{\\ast}$ the magnetization for $B||[111]$ displays a two step behavior\nsignalling the breaking of the ice rules.", "category": "cond-mat_dis-nn" }, { "text": "Method to solve quantum few-body problems with artificial neural\n networks: A machine learning technique to obtain the ground states of quantum few-body\nsystems using artificial neural networks is developed. Bosons in continuous\nspace are considered and a neural network is optimized in such a way that when\nparticle positions are input into the network, the ground-state wave function\nis output from the network. The method is applied to the Calogero-Sutherland\nmodel in one-dimensional space and Efimov bound states in three-dimensional\nspace.", "category": "cond-mat_dis-nn" }, { "text": "Comprehensive study of the critical behavior in the diluted\n antiferromagnet in a field: We study the critical behavior of the Diluted Antiferromagnet in a Field with\nthe Tethered Monte Carlo formalism. We compute the critical exponents\n(including the elusive hyperscaling violations exponent $\\theta$). Our results\nprovide a comprehensive description of the phase transition and clarify the\ninconsistencies between previous experimental and theoretical work. To do so,\nour method addresses the usual problems of numerical work (large tunneling\nbarriers and self-averaging violations).", "category": "cond-mat_dis-nn" }, { "text": "Unraveling the nature of carrier mediated ferromagnetism in diluted\n magnetic semiconductors: After more than a decade of intensive research in the field of diluted\nmagnetic semiconductors (DMS), the nature and origin of ferromagnetism,\nespecially in III-V compounds is still controversial. Many questions and open\nissues are under intensive debates. Why after so many years of investigations\nMn doped GaAs remains the candidate with the highest Curie temperature among\nthe broad family of III-V materials doped with transition metal (TM) impurities\n? How can one understand that these temperatures are almost two orders of\nmagnitude larger than that of hole doped (Zn,Mn)Te or (Cd,Mn)Se? Is there any\nintrinsic limitation or is there any hope to reach in the dilute regime room\ntemperature ferromagnetism? How can one explain the proximity of (Ga,Mn)As to\nthe metal-insulator transition and the change from\nRuderman-Kittel-Kasuya-Yosida (RKKY) couplings in II-VI compounds to double\nexchange type in (Ga,Mn)N? In spite of the great success of density functional\ntheory based studies to provide accurately the critical temperatures in various\ncompounds, till very lately a theory that provides a coherent picture and\nunderstanding of the underlying physics was still missing. Recently, within a\nminimal model it has been possible to show that among the physical parameters,\nthe key one is the position of the TM acceptor level. By tuning the value of\nthat parameter, one is able to explain quantitatively both magnetic and\ntransport properties in a broad family of DMS. We will see that this minimal\nmodel explains in particular the RKKY nature of the exchange in\n(Zn,Mn)Te/(Cd,Mn)Te and the double exchange type in (Ga,Mn)N and simultaneously\nthe reason why (Ga,Mn)As exhibits the highest critical temperature among both\nII-VI and III-V DMS.", "category": "cond-mat_dis-nn" }, { "text": "Thermodynamics of bidirectional associative memories: In this paper we investigate the equilibrium properties of bidirectional\nassociative memories (BAMs). Introduced by Kosko in 1988 as a generalization of\nthe Hopfield model to a bipartite structure, the simplest architecture is\ndefined by two layers of neurons, with synaptic connections only between units\nof different layers: even without internal connections within each layer,\ninformation storage and retrieval are still possible through the reverberation\nof neural activities passing from one layer to another. We characterize the\ncomputational capabilities of a stochastic extension of this model in the\nthermodynamic limit, by applying rigorous techniques from statistical physics.\nA detailed picture of the phase diagram at the replica symmetric level is\nprovided, both at finite temperature and in the noiseless regimes. Also for the\nlatter, the critical load is further investigated up to one step of replica\nsymmetry breaking. An analytical and numerical inspection of the transition\ncurves (namely critical lines splitting the various modes of operation of the\nmachine) is carried out as the control parameters - noise, load and asymmetry\nbetween the two layer sizes - are tuned. In particular, with a finite asymmetry\nbetween the two layers, it is shown how the BAM can store information more\nefficiently than the Hopfield model by requiring less parameters to encode a\nfixed number of patterns. Comparisons are made with numerical simulations of\nneural dynamics. Finally, a low-load analysis is carried out to explain the\nretrieval mechanism in the BAM by analogy with two interacting Hopfield models.\nA potential equivalence with two coupled Restricted Boltmzann Machines is also\ndiscussed.", "category": "cond-mat_dis-nn" }, { "text": "Quasicrystalline Bose glass in the absence of disorder and quasidisorder: We study the low-temperature phases of interacting bosons on a\ntwo-dimensional quasicrystalline lattice. By means of numerically exact Path\nIntegral Monte Carlo simulations, we show that for sufficiently weak\ninteractions the system is a homogeneous Bose-Einstein condensate, which\ndevelops density modulations for increasing filling factor. The simultaneous\noccurrence of sizeable condensate fraction and density modulation can be\ninterpreted as the analogous, in a quasicrystalline lattice, of supersolid\nphases occurring in conventional periodic lattices. For sufficiently large\ninteraction strength and particle density, global condensation is lost and\nquantum exchanges are restricted to specific spatial regions. The emerging\nquantum phase is therefore a Bose Glass, which here is stabilized in the\nabsence of any source of disorder or quasidisorder, purely as a result of the\ninterplay between quantum effects, particle interactions and quasicrystalline\nsubstrate. This finding clearly indicates that (quasi)disorder is not essential\nto observe Bose Glass physics. Our results are of interest for ongoing\nexperiments on (quasi)disorder-free quasicrystalline lattices.", "category": "cond-mat_dis-nn" }, { "text": "Bose-Bose mixtures in a weak-disorder potential: Fluctuations and\n superfluidity: We study the properties of a homogeneous dilute Bose-Bose gas in a\nweak-disorder potential at zero temperature. By using the perturbation theory,\nwe calculate the disorder corrections to the condensate density, the equation\nof state, the compressibility, and the superfluid density as a function of\ndensity, strength of disorder, and miscibility parameter. It is found that the\ndisorder potential may lead to modifying the miscibility-immiscibility\ncondition and a full miscible phase turns out to be impossible in the presence\nof the disorder. We show that the intriguing interplay of the disorder and\nintra- and interspecies interactions may strongly influence the localization of\neach component, the quantum fluctuations, and the compressibility, as well as\nthe superfluidity of the system.", "category": "cond-mat_dis-nn" }, { "text": "Universality of the Wigner time delay distribution for one-dimensional\n random potentials: We show that the distribution of the time delay for one-dimensional random\npotentials is universal in the high energy or weak disorder limit. Our\nanalytical results are in excellent agreement with extensive numerical\nsimulations carried out on samples whose sizes are large compared to the\nlocalisation length (localised regime). The case of small samples is also\ndiscussed (ballistic regime). We provide a physical argument which explains in\na quantitative way the origin of the exponential divergence of the moments. The\noccurence of a log-normal tail for finite size systems is analysed. Finally, we\npresent exact results in the low energy limit which clearly show a departure\nfrom the universal behaviour.", "category": "cond-mat_dis-nn" }, { "text": "Interaction-enhanced integer quantum Hall effect in disordered systems: We study transport properties and topological phase transition in\ntwo-dimensional interacting disordered systems. Within dynamical mean-field\ntheory, we derive the Hall conductance, which is quantized and serves as a\ntopological invariant for insulators, even when the energy gap is closed by\nlocalized states. In the spinful Harper-Hofstadter-Hatsugai model, in the\ntrivial insulator regime, we find that the repulsive on-site interaction can\nassist weak disorder to induce the integer quantum Hall effect, while in the\ntopologically non-trivial regime, it impedes Anderson localization. Generally,\nthe interaction broadens the regime of the topological phase in the disordered\nsystem.", "category": "cond-mat_dis-nn" }, { "text": "Random matrices with row constraints and eigenvalue distributions of\n graph Laplacians: Symmetric matrices with zero row sums occur in many theoretical settings and\nin real-life applications. When the offdiagonal elements of such matrices are\ni.i.d. random variables and the matrices are large, the eigenvalue\ndistributions converge to a peculiar universal curve\n$p_{\\mathrm{zrs}}(\\lambda)$ that looks like a cross between the Wigner\nsemicircle and a Gaussian distribution. An analytic theory for this curve,\noriginally due to Fyodorov, can be developed using supersymmetry-based\ntechniques.\n We extend these derivations to the case of sparse matrices, including the\nimportant case of graph Laplacians for large random graphs with $N$ vertices of\nmean degree $c$. In the regime $1\\ll c\\ll N$, the eigenvalue distribution of\nthe ordinary graph Laplacian (diffusion with a fixed transition rate per edge)\ntends to a shifted and scaled version of $p_{\\mathrm{zrs}}(\\lambda)$, centered\nat $c$ with width $\\sim\\sqrt{c}$. At smaller $c$, this curve receives\ncorrections in powers of $1/\\sqrt{c}$ accurately captured by our theory. For\nthe normalized graph Laplacian (diffusion with a fixed transition rate per\nvertex), the large $c$ limit is a shifted and scaled Wigner semicircle, again\nwith corrections captured by our analysis.", "category": "cond-mat_dis-nn" }, { "text": "Note: Effect of localization on mean-field density of state near jamming: We discuss the effects of the localized modes on the density of state\n$D(\\omega)$ by introducing the probability distribution function of the\nproximity to the marginal stability. Our theoretical treatment reproduces the\nnumerical results in finite dimensions near the jamming point., in particular,\nsuccessfully captures the novel $D(\\omega)\\sim \\omega^4$ scaling including its\npressure dependence of the pre-factor.", "category": "cond-mat_dis-nn" }, { "text": "Phase Transition in the Random Anisotropy Model: The influence of a local anisotropy of random orientation on a ferromagnetic\nphase transition is studied for two cases of anisotropy axis distribution. To\nthis end a model of a random anisotropy magnet is analyzed by means of the\nfield theoretical renormalization group approach in two loop approximation\nrefined by a resummation of the asymptotic series. The one-loop result of\nAharony indicating the absence of a second-order phase transition for an\nisotropic distribution of random anisotropy axis at space dimension $d<4$ is\ncorroborated. For a cubic distribution the accessible stable fixed point leads\nto disordered Ising-like critical exponents.", "category": "cond-mat_dis-nn" }, { "text": "Atomistic simulation of nearly defect-free models of amorphous silicon:\n An information-based approach: We present an information-based total-energy optimization method to produce\nnearly defect-free structural models of amorphous silicon. Using geometrical,\nstructural and topological information from disordered tetrahedral networks, we\nhave shown that it is possible to generate structural configurations of\namorphous silicon, which are superior than the models obtained from\nconventional reverse Monte Carlo and molecular-dynamics simulations. The new\ndata-driven hybrid approach presented here is capable of producing atomistic\nmodels with structural and electronic properties which are on a par with those\nobtained from the modified Wooten-Winer-Weaire (WWW) models of amorphous\nsilicon. Structural, electronic and thermodynamic properties of the hybrid\nmodels are compared with the best dynamical models obtained from using\nmachine-intelligence-based potentials and efficient classical\nmolecular-dynamics simulations, reported in the recent literature. We have\nshown that, together with the WWW models, our hybrid models represent one of\nthe best structural models so far produced by total-energy-based Monte Carlo\nmethods in conjunction with experimental diffraction data and a few structural\nconstraints.", "category": "cond-mat_dis-nn" }, { "text": "Localization crossover and subdiffusive transport in a classical\n facilitated network model of a disordered, interacting quantum spin chain: We consider the random-field Heisenberg model, a paradigmatic model for\nmany-body localization (MBL), and add a Markovian dephasing bath coupled to the\nAnderson orbitals of the model's non-interacting limit. We map this system to a\nclassical facilitated hopping model that is computationally tractable for large\nsystem sizes, and investigate its dynamics. The classical model exhibits a\nrobust crossover between an ergodic (thermal) phase and a frozen (localized)\nphase. The frozen phase is destabilized by thermal subregions (bubbles), which\nthermalize surrounding sites by providing a fluctuating interaction energy and\nso enable off-resonance particle transport. Investigating steady state\ntransport, we observe that the interplay between thermal and frozen bubbles\nleads to a clear transition between diffusive and subdiffusive regimes. This\nphenomenology both describes the MBL system coupled to a bath, and provides a\nclassical analogue for the many-body localization transition in the\ncorresponding quantum model, in that the classical model displays long local\nmemory times. It also highlights the importance of the details of the bath\ncoupling in studies of MBL systems coupled to thermal environments.", "category": "cond-mat_dis-nn" }, { "text": "Spatial Structure of the Internet Traffic: The Internet infrastructure is not virtual: its distribution is dictated by\nsocial, geographical, economical, or political constraints. However, the\ninfrastructure's design does not determine entirely the information traffic and\ndifferent sources of complexity such as the intrinsic heterogeneity of the\nnetwork or human practices have to be taken into account. In order to manage\nthe Internet expansion, plan new connections or optimize the existing ones, it\nis thus critical to understand correlations between emergent global statistical\npatterns of Internet activity and human factors. We analyze data from the\nFrench national `Renater' network which has about two millions users and which\nconsists in about 30 interconnected routers located in different regions of\nFrance and we report the following results. The Internet flow is strongly\nlocalized: most of the traffic takes place on a `spanning' network connecting a\nsmall number of routers which can be classified either as `active centers'\nlooking for information or `databases' providing information. We also show that\nthe Internet activity of a region increases with the number of published papers\nby laboratories of that region, demonstrating the positive impact of the Web on\nscientific activity and illustrating quantitatively the adage `the more you\nread, the more you write'.", "category": "cond-mat_dis-nn" }, { "text": "Anderson localization in Bose-Einstein condensates: The understanding of disordered quantum systems is still far from being\ncomplete, despite many decades of research on a variety of physical systems. In\nthis review we discuss how Bose-Einstein condensates of ultracold atoms in\ndisordered potentials have opened a new window for studying fundamental\nphenomena related to disorder. In particular, we point our attention to recent\nexperimental studies on Anderson localization and on the interplay of disorder\nand weak interactions. These realize a very promising starting point for a\ndeeper understanding of the complex behaviour of interacting, disordered\nsystems.", "category": "cond-mat_dis-nn" }, { "text": "q-Random Matrix Ensembles: Theory of Random Matrix Ensembles have proven to be a useful tool in the\nstudy of the statistical distribution of energy or transmission levels of a\nwide variety of physical systems. We give an overview of certain\nq-generalizations of the Random Matrix Ensembles, which were first introduced\nin connection with the statistical description of disordered quantum\nconductors.", "category": "cond-mat_dis-nn" }, { "text": "Spectra of Modular and Small-World Matrices: We compute spectra of symmetric random matrices describing graphs with\ngeneral modular structure and arbitrary inter- and intra-module degree\ndistributions, subject only to the constraint of finite mean connectivities. We\nalso evaluate spectra of a certain class of small-world matrices generated from\nrandom graphs by introducing short-cuts via additional random connectivity\ncomponents. Both adjacency matrices and the associated graph Laplacians are\ninvestigated. For the Laplacians, we find Lifshitz type singular behaviour of\nthe spectral density in a localised region of small $|\\lambda|$ values. In the\ncase of modular networks, we can identify contributions local densities of\nstate from individual modules. For small-world networks, we find that the\nintroduction of short cuts can lead to the creation of satellite bands outside\nthe central band of extended states, exhibiting only localised states in the\nband-gaps. Results for the ensemble in the thermodynamic limit are in excellent\nagreement with those obtained via a cavity approach for large finite single\ninstances, and with direct diagonalisation results.", "category": "cond-mat_dis-nn" }, { "text": "Current Redistribution in Resistor Networks: Fat-Tail Statistics in\n Regular and Small-World Networks: The redistribution of electrical currents in resistor networks after\nsingle-bond failures is analyzed in terms of current-redistribution factors\nthat are shown to depend only on the topology of the network and on the values\nof the bond resistances. We investigate the properties of these\ncurrent-redistribution factors for regular network topologies (e.g.\n$d$-dimensional hypercubic lattices) as well as for small-world networks. In\nparticular, we find that the statistics of the current redistribution factors\nexhibits a fat-tail behavior, which reflects the long-range nature of the\ncurrent redistribution as determined by Kirchhoff's circuit laws.", "category": "cond-mat_dis-nn" }, { "text": "Study of the de Almeida-Thouless line using power-law diluted\n one-dimensional Ising spin glasses: We test for the existence of a spin-glass phase transition, the de\nAlmeida-Thouless line, in an externally-applied (random) magnetic field by\nperforming Monte Carlo simulations on a power-law diluted one-dimensional Ising\nspin glass for very large system sizes. We find that an Almeida-Thouless line\nonly occurs in the mean field regime, which corresponds, for a short-range spin\nglass, to dimension d larger than 6.", "category": "cond-mat_dis-nn" }, { "text": "Interface Energy in the Edwards-Anderson model: We numerically investigate the spin glass energy interface problem in three\ndimensions. We analyze the energy cost of changing the overlap from -1 to +1 at\none boundary of two coupled systems (in the other boundary the overlap is kept\nfixed to +1). We implement a parallel tempering algorithm that simulate finite\ntemperature systems and work with both cubic lattices and parallelepiped with\nfixed aspect ratio. We find results consistent with a lower critical dimension\n$D_c=2.5$. The results show a good agreement with the mean field theory\npredictions.", "category": "cond-mat_dis-nn" }, { "text": "Low-rank combinatorial optimization and statistical learning by spatial\n photonic Ising machine: The spatial photonic Ising machine (SPIM) [D. Pierangeli et al., Phys. Rev.\nLett. 122, 213902 (2019)] is a promising optical architecture utilizing spatial\nlight modulation for solving large-scale combinatorial optimization problems\nefficiently. The primitive version of the SPIM, however, can accommodate Ising\nproblems with only rank-one interaction matrices. In this Letter, we propose a\nnew computing model for the SPIM that can accommodate any Ising problem without\nchanging its optical implementation. The proposed model is particularly\nefficient for Ising problems with low-rank interaction matrices, such as\nknapsack problems. Moreover, it acquires the learning ability of Boltzmann\nmachines. We demonstrate that learning, classification, and sampling of the\nMNIST handwritten digit images are achieved efficiently using the model with\nlow-rank interactions. Thus, the proposed model exhibits higher practical\napplicability to various problems of combinatorial optimization and statistical\nlearning, without losing the scalability inherent in the SPIM architecture.", "category": "cond-mat_dis-nn" }, { "text": "Statistics of the Mesoscopic Field: We find in measurements of microwave transmission through quasi-1D dielectric\nsamples for both diffusive and localized waves that the field normalized by the\nsquare root of the spatially averaged flux in a given sample configuration is a\nGaussian random process with position, polarization, frequency, and time. As a\nresult, the probability distribution of the field in the random ensemble is a\nmixture of Gaussian functions weighted by the distribution of total\ntransmission, while its correlation function is a product of correlators of the\nGaussian field and the square root of the total transmission.", "category": "cond-mat_dis-nn" }, { "text": "Slow conductance relaxations; Distinguishing the Electron Glass from\n extrinsic mechanisms: Slow conductance relaxations are observable in a many condensed matter\nsystems. These are sometimes described as manifestations of a glassy phase. The\nunderlying mechanisms responsible for the slow dynamics are often due to\nstructural changes which modify the potential landscape experienced by the\ncharge-carriers and thus are reflected in the conductance. Sluggish conductance\ndynamics may however originate from the interplay between electron-electron\ninteractions and quenched disorder. Examples for both scenarios and the\nexperimental features that should help to distinguish between them are shown\nand discussed. In particular, it is suggested that the `memory-dip' observable\nthrough field-effect measurements is a characteristic signature of the inherent\nelectron-glass provided it obeys certain conditions.", "category": "cond-mat_dis-nn" }, { "text": "Influence of synaptic depression on memory storage capacity: Synaptic efficacy between neurons is known to change within a short time\nscale dynamically. Neurophysiological experiments show that high-frequency\npresynaptic inputs decrease synaptic efficacy between neurons. This phenomenon\nis called synaptic depression, a short term synaptic plasticity. Many\nresearchers have investigated how the synaptic depression affects the memory\nstorage capacity. However, the noise has not been taken into consideration in\ntheir analysis. By introducing \"temperature\", which controls the level of the\nnoise, into an update rule of neurons, we investigate the effects of synaptic\ndepression on the memory storage capacity in the presence of the noise. We\nanalytically compute the storage capacity by using a statistical mechanics\ntechnique called Self Consistent Signal to Noise Analysis (SCSNA). We find that\nthe synaptic depression decreases the storage capacity in the case of finite\ntemperature in contrast to the case of the low temperature limit, where the\nstorage capacity does not change.", "category": "cond-mat_dis-nn" }, { "text": "Simulated annealing, optimization, searching for ground states: The chapter starts with a historical summary of first attempts to optimize\nthe spin glass Hamiltonian, comparing it to recent results on searching largest\ncliques in random graphs. Exact algorithms to find ground states in generic\nspin glass models are then explored in Section 1.2, while Section 1.3 is\ndedicated to the bidimensional case where polynomial algorithms exist and allow\nfor the study of much larger systems. Finally Section 1.4 presents a summary of\nresults for the assignment problem where the finite size corrections for the\nground state can be studied in great detail.", "category": "cond-mat_dis-nn" }, { "text": "Sequence Nets: We study a new class of networks, generated by sequences of letters taken\nfrom a finite alphabet consisting of $m$ letters (corresponding to $m$ types of\nnodes) and a fixed set of connectivity rules. Recently, it was shown how a\nbinary alphabet might generate threshold nets in a similar fashion [Hagberg et\nal., Phys. Rev. E 74, 056116 (2006)]. Just like threshold nets, sequence nets\nin general possess a modular structure reminiscent of everyday life nets, and\nare easy to handle analytically (i.e., calculate degree distribution, shortest\npaths, betweenness centrality, etc.). Exploiting symmetry, we make a full\nclassification of two- and three-letter sequence nets, discovering two new\nclasses of two-letter sequence nets. The new sequence nets retain many of the\ndesirable analytical properties of threshold nets while yielding richer\npossibilities for the modeling of everyday life complex networks more\nfaithfully.", "category": "cond-mat_dis-nn" }, { "text": "On the critical behavior of the Susceptible-Infected-Recovered (SIR)\n model on a square lattice: By means of numerical simulations and epidemic analysis, the transition point\nof the stochastic, asynchronous Susceptible-Infected-Recovered (SIR) model on a\nsquare lattice is found to be c_0=0.1765005(10), where c is the probability a\nchosen infected site spontaneously recovers rather than tries to infect one\nneighbor. This point corresponds to an infection/recovery rate of lambda_c =\n(1-c_0)/c_0 = 4.66571(3) and a net transmissibility of (1-c_0)/(1 + 3 c_0) =\n0.538410(2), which falls between the rigorous bounds of the site and bond\nthresholds. The critical behavior of the model is consistent with the 2-d\npercolation universality class, but local growth probabilities differ from\nthose of dynamic percolation cluster growth, as is demonstrated explicitly.", "category": "cond-mat_dis-nn" }, { "text": "Slow Nonthermalizing Dynamics in a Quantum Spin Glass: Spin glasses and many-body localization (MBL) are prime examples of\nergodicity breaking, yet their physical origin is quite different: the former\nphase arises due to rugged classical energy landscape, while the latter is a\nquantum-interference effect. Here we study quantum dynamics of an isolated 1d\nspin-glass under application of a transverse field. At high energy densities,\nthe system is ergodic, relaxing via resonance avalanche mechanism, that is also\nresponsible for the destruction of MBL in non-glassy systems with power-law\ninteractions. At low energy densities, the interaction-induced fields obtain a\npower-law soft gap, making the resonance avalanche mechanism inefficient. This\nleads to the persistence of the spin-glass order, as demonstrated by resonance\nanalysis and by numerical studies. A small fraction of resonant spins forms a\nthermalizing system with long-range entanglement, making this regime distinct\nfrom the conventional MBL. The model considered can be realized in systems of\ntrapped ions, opening the door to investigating slow quantum dynamics induced\nby glassiness.", "category": "cond-mat_dis-nn" }, { "text": "Universal crossover from ground state to excited-state quantum\n criticality: We study the nonequilibrium properties of a nonergodic random quantum chain\nin which highly excited eigenstates exhibit critical properties usually\nassociated with quantum critical ground states. The ground state and excited\nstates of this system belong to different universality classes, characterized\nby infinite-randomness quantum critical behavior. Using strong-disorder\nrenormalization group techniques, we show that the crossover between the zero\nand finite energy density regimes is universal. We analytically derive a flow\nequation describing the unitary dynamics of this isolated system at finite\nenergy density from which we obtain universal scaling functions along the\ncrossover.", "category": "cond-mat_dis-nn" }, { "text": "Breakdown of Dynamical Scale Invariance in the Coarsening of Fractal\n Clusters: We extend a previous analysis [PRL {\\bf 80}, 4693 (1998)] of breakdown of\ndynamical scale invariance in the coarsening of two-dimensional DLAs\n(diffusion-limited aggregates) as described by the Cahn-Hilliard equation.\nExistence of a second dynamical length scale, predicted earlier, is\nestablished. Having measured the \"solute mass\" outside the cluster versus time,\nwe obtain a third dynamical exponent. An auxiliary problem of the dynamics of a\nslender bar (that acquires a dumbbell shape) is considered. A simple scenario\nof coarsening of fractal clusters with branching structure is suggested that\nemploys the dumbbell dynamics results. This scenario involves two dynamical\nlength scales: the characteristic width and length of the cluster branches. The\npredicted dynamical exponents depend on the (presumably invariant) fractal\ndimension of the cluster skeleton. In addition, a robust theoretical estimate\nfor the third dynamical exponent is obtained. Exponents found numerically are\nin reasonable agreement with these predictions.", "category": "cond-mat_dis-nn" }, { "text": "Real space information from Fluctuation electron microscopy:\n Applications to amorphous silicon: Ideal models of complex materials must satisfy all available information\nabout the system. Generally, this information consists of experimental data,\ninformation implicit to sophisticated interatomic interactions and potentially\nother {\\it a priori} information. By jointly imposing first-principles or\ntight-binding information in conjunction with experimental data, we have\ndeveloped a method: Experimentally Constrained Molecular Relaxation (ECMR) that\nuses {\\it all} of the information available. We apply the method to model\nmedium range order in amorphous silicon using Fluctuation Electron microscopy\n(FEM) data as experimental information. The paracrystalline model of medium\nrange order is examined, and a new model based on voids in amorphous silicon is\nproposed. Our work suggests that films of amorphous silicon showing medium\nrange order (in FEM experiments) can be accurately represented by a continuous\nrandom network model with inhomogeneities consisting of ordered grains and\nvoids dispersed in the network.", "category": "cond-mat_dis-nn" }, { "text": "Network Synchronization, Diffusion, and the Paradox of Heterogeneity: Many complex networks display strong heterogeneity in the degree\n(connectivity) distribution. Heterogeneity in the degree distribution often\nreduces the average distance between nodes but, paradoxically, may suppress\nsynchronization in networks of oscillators coupled symmetrically with uniform\ncoupling strength. Here we offer a solution to this apparent paradox. Our\nanalysis is partially based on the identification of a diffusive process\nunderlying the communication between oscillators and reveals a striking\nrelation between this process and the condition for the linear stability of the\nsynchronized states. We show that, for a given degree distribution, the maximum\nsynchronizability is achieved when the network of couplings is weighted and\ndirected, and the overall cost involved in the couplings is minimum. This\nenhanced synchronizability is solely determined by the mean degree and does not\ndepend on the degree distribution and system size. Numerical verification of\nthe main results is provided for representative classes of small-world and\nscale-free networks.", "category": "cond-mat_dis-nn" }, { "text": "Slow conductance relaxations; Distinguishing the Electron Glass from\n extrinsic mechanisms: Slow conductance relaxations are observable in a many condensed matter\nsystems. These are sometimes described as manifestations of a glassy phase. The\nunderlying mechanisms responsible for the slow dynamics are often due to\nstructural changes which modify the potential landscape experienced by the\ncharge-carriers and thus are reflected in the conductance. Sluggish conductance\ndynamics may however originate from the interplay between electron-electron\ninteractions and quenched disorder. Examples for both scenarios and the\nexperimental features that should help to distinguish between them are shown\nand discussed. In particular, it is suggested that the `memory-dip' observable\nthrough field-effect measurements is a characteristic signature of the inherent\nelectron-glass provided it obeys certain conditions.", "category": "cond-mat_dis-nn" }, { "text": "Free energy fluctuations and chaos in the Sherrington-Kirkpatrick model: The sample-to-sample fluctuations Delta F_N of the free energy in the\nSherrington-Kirkpatrick model are shown rigorously to be related to bond chaos.\nVia this connection, the fluctuations become analytically accessible by replica\nmethods. The replica calculation for bond chaos shows that the exponent mu\ngoverning the growth of the fluctuations with system size N, i.e. Delta F_N\nN^mu, is bounded by mu <= 1/4.", "category": "cond-mat_dis-nn" }, { "text": "Network synchronization: Optimal and Pessimal Scale-Free Topologies: By employing a recently introduced optimization algorithm we explicitely\ndesign optimally synchronizable (unweighted) networks for any given scale-free\ndegree distribution. We explore how the optimization process affects\ndegree-degree correlations and observe a generic tendency towards\ndisassortativity. Still, we show that there is not a one-to-one correspondence\nbetween synchronizability and disassortativity. On the other hand, we study the\nnature of optimally un-synchronizable networks, that is, networks whose\ntopology minimizes the range of stability of the synchronous state. The\nresulting ``pessimal networks'' turn out to have a highly assortative\nstring-like structure. We also derive a rigorous lower bound for the Laplacian\neigenvalue ratio controlling synchronizability, which helps understanding the\nimpact of degree correlations on network synchronizability.", "category": "cond-mat_dis-nn" }, { "text": "Soft-margin classification of object manifolds: A neural population responding to multiple appearances of a single object\ndefines a manifold in the neural response space. The ability to classify such\nmanifolds is of interest, as object recognition and other computational tasks\nrequire a response that is insensitive to variability within a manifold. Linear\nclassification of object manifolds was previously studied for max-margin\nclassifiers. Soft-margin classifiers are a larger class of algorithms and\nprovide an additional regularization parameter used in applications to optimize\nperformance outside the training set by balancing between making fewer training\nerrors and learning more robust classifiers. Here we develop a mean-field\ntheory describing the behavior of soft-margin classifiers applied to object\nmanifolds. Analyzing manifolds with increasing complexity, from points through\nspheres to general manifolds, a mean-field theory describes the expected value\nof the linear classifier's norm, as well as the distribution of fields and\nslack variables. By analyzing the robustness of the learned classification to\nnoise, we can predict the probability of classification errors and their\ndependence on regularization, demonstrating a finite optimal choice. The theory\ndescribes a previously unknown phase transition, corresponding to the\ndisappearance of a non-trivial solution, thus providing a soft version of the\nwell-known classification capacity of max-margin classifiers.", "category": "cond-mat_dis-nn" }, { "text": "Localization of vibrational modes in high-entropy oxides: The recently-discovered high-entropy oxides offer a paradoxical combination\nof crystalline arrangement and high disorder. They differ qualitatively from\nestablished paradigms for disordered solids such as glasses and alloys. In\nthese latter systems, it is well known that disorder induces localized\nvibrational excitations. In this article, we explore the possibility of\ndisorder-induced localization in (MgCoCuNiZn)O, the prototypical high-entropy\noxide with rock-salt structure. To describe phononic excitations, we model the\ninteratomic potentials for the cation-oxygen interactions by fitting to the\nphysical properties of the parent binary oxides. We validate our model against\nthe experimentally determined crystal structure, bond lengths, and optical\nconductivity. The resulting phonon spectrum shows wave-like propagating modes\nat low energies and localized modes at high energies. Localization is reflected\nin signatures such as participation ratio and correlation amplitude. Finally,\nwe explore the possibility of increased mass disorder in the oxygen sublattice.\nAdmixing sulphur or tellurium atoms with oxygen enhances localization. It even\nleads to localized modes in the middle of the spectrum. Our results suggest\nthat high-entropy oxides are a promising platform to study Anderson\nlocalization of phonons.", "category": "cond-mat_dis-nn" }, { "text": "Distribution of velocities in an avalanche, and related quantities:\n Theory and numerical verification: We study several probability distributions relevant to the avalanche dynamics\nof elastic interfaces driven on a random substrate: The distribution of size,\nduration, lateral extension or area, as well as velocities. Results from the\nfunctional renormalization group and scaling relations involving two\nindependent exponents, roughness $\\zeta$, and dynamics $z$, are confronted to\nhigh-precision numerical simulations of an elastic line with short-range\nelasticity, i.e. of internal dimension $d=1$. The latter are based on a novel\nstochastic algorithm which generates its disorder on the fly. Its precision\ngrows linearly in the time-discretization step, and it is parallelizable. Our\nresults show good agreement between theory and numerics, both for the critical\nexponents as for the scaling functions. In particular, the prediction ${\\sf a}\n= 2 - \\frac{2}{d+ \\zeta - z}$ for the velocity exponent is confirmed with good\naccuracy.", "category": "cond-mat_dis-nn" }, { "text": "Localization of weakly disordered flat band states: Certain tight binding lattices host macroscopically degenerate flat spectral\nbands. Their origin is rooted in local symmetries of the lattice, with\ndestructive interference leading to the existence of compact localized\neigenstates. We study the robustness of this localization to disorder in\ndifferent classes of flat band lattices in one and two dimensions. Depending on\nthe flat band class, the flat band states can either be robust, preserving\ntheir strong localization for weak disorder W, or they are destroyed and\nacquire large localization lengths $\\xi$ that diverge with a variety of\nunconventional exponents $\\nu$, $\\xi \\sim 1/W^{\\nu}$.", "category": "cond-mat_dis-nn" }, { "text": "Phase Ordering and Onset of Collective Behavior in Chaotic Coupled Map\n Lattices: The phase ordering properties of lattices of band-chaotic maps coupled\ndiffusively with some coupling strength $g$ are studied in order to determine\nthe limit value $g_e$ beyond which multistability disappears and non-trivial\ncollective behavior is observed. The persistence of equivalent discrete spin\nvariables and the characteristic length of the patterns observed scale\nalgebraically with time during phase ordering. The associated exponents vary\ncontinuously with $g$ but remain proportional to each other, with a ratio close\nto that of the time-dependent Ginzburg-Landau equation. The corresponding\nindividual values seem to be recovered in the space-continuous limit.", "category": "cond-mat_dis-nn" }, { "text": "Statistical Mechanical Development of a Sparse Bayesian Classifier: The demand for extracting rules from high dimensional real world data is\nincreasing in various fields. However, the possible redundancy of such data\nsometimes makes it difficult to obtain a good generalization ability for novel\nsamples. To resolve this problem, we provide a scheme that reduces the\neffective dimensions of data by pruning redundant components for bicategorical\nclassification based on the Bayesian framework. First, the potential of the\nproposed method is confirmed in ideal situations using the replica method.\nUnfortunately, performing the scheme exactly is computationally difficult. So,\nwe next develop a tractable approximation algorithm, which turns out to offer\nnearly optimal performance in ideal cases when the system size is large.\nFinally, the efficacy of the developed classifier is experimentally examined\nfor a real world problem of colon cancer classification, which shows that the\ndeveloped method can be practically useful.", "category": "cond-mat_dis-nn" }, { "text": "Critical Line in Random Threshold Networks with Inhomogeneous Thresholds: We calculate analytically the critical connectivity $K_c$ of Random Threshold\nNetworks (RTN) for homogeneous and inhomogeneous thresholds, and confirm the\nresults by numerical simulations. We find a super-linear increase of $K_c$ with\nthe (average) absolute threshold $|h|$, which approaches $K_c(|h|) \\sim\nh^2/(2\\ln{|h|})$ for large $|h|$, and show that this asymptotic scaling is\nuniversal for RTN with Poissonian distributed connectivity and threshold\ndistributions with a variance that grows slower than $h^2$. Interestingly, we\nfind that inhomogeneous distribution of thresholds leads to increased\npropagation of perturbations for sparsely connected networks, while for densely\nconnected networks damage is reduced; the cross-over point yields a novel,\ncharacteristic connectivity $K_d$, that has no counterpart in Boolean networks.\nLast, local correlations between node thresholds and in-degree are introduced.\nHere, numerical simulations show that even weak (anti-)correlations can lead to\na transition from ordered to chaotic dynamics, and vice versa. It is shown that\nthe naive mean-field assumption typical for the annealed approximation leads to\nfalse predictions in this case, since correlations between thresholds and\nout-degree that emerge as a side-effect strongly modify damage propagation\nbehavior.", "category": "cond-mat_dis-nn" }, { "text": "Hyperscaling breakdown and Ising Spin Glasses: the Binder cumulant: Among the Renormalization Group Theory scaling rules relating critical\nexponents, there are hyperscaling rules involving the dimension of the system.\nIt is well known that in Ising models hyperscaling breaks down above the upper\ncritical dimension. It was shown by M. Schwartz [Europhys. Lett. {\\bf 15}, 777\n(1991)] that the standard Josephson hyperscaling rule can also break down in\nIsing systems with quenched random interactions. A related Renormalization\nGroup Theory hyperscaling rule links the critical exponents for the normalized\nBinder cumulant and the correlation length in the thermodynamic limit. An\nappropriate scaling approach for analyzing measurements from criticality to\ninfinite temperature is first outlined. Numerical data on the scaling of the\nnormalized correlation length and the normalized Binder cumulant are shown for\nthe canonical Ising ferromagnet model in dimension three where hyperscaling\nholds, for the Ising ferromagnet in dimension five (so above the upper critical\ndimension) where hyperscaling breaks down, and then for Ising spin glass models\nin dimension three where the quenched interactions are random. For the Ising\nspin glasses there is a breakdown of the normalized Binder cumulant\nhyperscaling relation in the thermodynamic limit regime, with a return to size\nindependent Binder cumulant values in the finite-size scaling regime around the\ncritical region.", "category": "cond-mat_dis-nn" }, { "text": "Closed-Form Density of States and Localization Length for a\n Non-Hermitian Disordered System: We calculate the Lyapunov exponent for the non-Hermitian Zakharov-Shabat\neigenvalue problem corresponding to the attractive non-linear Schroedinger\nequation with a Gaussian random pulse as initial value function. Using an\nextension of the Thouless formula to non-Hermitian random operators, we\ncalculate the corresponding average density of states. We analyze two cases,\none with circularly symmetric complex Gaussian pulses and the other with real\nGaussian pulses. We discuss the implications in the context of the information\ntransmission through non-linear optical fibers.", "category": "cond-mat_dis-nn" }, { "text": "Intrinsic versus super-rough anomalous scaling in spontaneous imbibition: We study spontaneous imbibition using a phase field model in a two\ndimensional system with a dichotomic quenched noise. By imposing a constant\npressure $\\mu_{a}<0$ at the origin, we study the case when the interface\nadvances at low velocities, obtaining the scaling exponents $z=3.0\\pm 0.1$,\n$\\alpha=1.50\\pm 0.02$ and $\\alpha_{loc}= 0.95\\pm 0.03$ within the intrinsic\nanomalous scaling scenario. These results are in quite good agreement with\nexperimental data recently published. Likewise, when we increase the interface\nvelocity, the resulting scaling exponents are $z=4.0 \\pm 0.1$, $\\alpha=1.25\\pm\n0.02$ and $\\alpha_{loc}= 0.95\\pm 0.03$. Moreover, we observe that the local\nproperties of the interface change from a super-rough to an intrinsic anomalous\ndescription when the contrast between the two values of the dichotomic noise is\nincreased. From a linearized interface equation we can compute analytically the\nglobal scaling exponents which are comparable to the numerical results,\nintroducing some properties of the quenched noise.", "category": "cond-mat_dis-nn" }, { "text": "Spatial Structures of Anomalously Localized States in Tail Regions at\n the Anderson Transition: We study spatial structures of anomalously localized states (ALS) in tail\nregions at the critical point of the Anderson transition in the two-dimensional\nsymplectic class. In order to examine tail structures of ALS, we apply the\nmultifractal analysis only for the tail region of ALS and compare with the\nwhole structure. It is found that the amplitude distribution in the tail region\nof ALS is multifractal and values of exponents characterizing multifractality\nare the same with those for typical multifractal wavefunctions in this\nuniversality class.", "category": "cond-mat_dis-nn" }, { "text": "Persistence of chirality in the Su-Schrieffer-Heeger model in the\n presence of on-site disorder: We consider the effects of on-site and hopping disorder on zero modes in the\nSu-Schrieffer-Heeger model. In the absence of disorder a domain wall gives rise\nto two chiral fractionalized bound states, one at the edge and one bound to the\ndomain wall. On-site disorder breaks the chiral symmetry, in contrast to\nhopping disorder. By using the polarization we find that on-site disorder has\nlittle effect on the chiral nature of the bound states for weak to moderate\ndisorder. We explore the behaviour of these bound states for strong disorder,\ncontrasting on-site and hopping disorder and connect our results to the\nlocalization properties of the bound states and to recent experiments.", "category": "cond-mat_dis-nn" }, { "text": "Far-from-equilibrium criticality in the Random Field Ising Model with\n Eshelby Interactions: We study a quasi-statically driven random field Ising model (RFIM) at zero\ntemperature with interactions mediated by the long-range anisotropic Eshelby\nkernel. Analogously to amorphous solids at their yielding transition, and\ndifferently from ferromagnetic and dipolar RFIMs, the model shows a\ndiscontinuous magnetization jump associated with the appearance of a band-like\nstructure for weak disorder and a continuous magnetization growth, yet\npunctuated by avalanches, for strong disorder. Through a finite-size scaling\nanalysis in 2 and 3 dimensions we find that the two regimes are separated by a\nfinite-disorder critical point which we characterize. We discuss similarities\nand differences between the present model and models of sheared amorphous\nsolids.", "category": "cond-mat_dis-nn" }, { "text": "Non-Hermitian disorder in two-dimensional optical lattices: In this paper, we study the properties of two-dimensional lattices in the\npresence of non-Hermitian disorder. In the context of coupled mode theory, we\nconsider random gain-loss distributions on every waveguide channel (on site\ndisorder). Our work provides a systematic study of the interplay between\ndisorder and non-Hermiticity. In particular, we study the eigenspectrum in the\ncomplex frequency plane and we examine the localization properties of the\neigenstates, either by the participation ratio or the level spacing, defined in\nthe complex plane. A modified level distribution function vs disorder seems to\nfit our computational results.", "category": "cond-mat_dis-nn" }, { "text": "Energy distribution of maxima and minima in a one-dimensional random\n system: We study the energy distribution of maxima and minima of a simple\none-dimensional disordered Hamiltonian. We find that in systems with short\nrange correlated disorder there is energy separation between maxima and minima,\nsuch that at fixed energy only one kind of stationary points is dominant in\nnumber over the other. On the other hand, in the case of systems with long\nrange correlated disorder maxima and minima are completely mixed.", "category": "cond-mat_dis-nn" }, { "text": "Monte Carlo Simulations of Doped, Diluted Magnetic Semiconductors - a\n System with Two Length Scales: We describe a Monte Carlo simulation study of the magnetic phase diagram of\ndiluted magnetic semiconductors doped with shallow impurities in the low\nconcentration regime. We show that because of a wide distribution of\ninteraction strengths, the system exhibits strong quantum effects in the\nmagnetically ordered phase. A discrete spin model, found to closely approximate\nthe quantum system, shows long relaxation times, and the need for specialized\ncluster algorithms for updating spin configurations. Results for a\nrepresentative system are presented.", "category": "cond-mat_dis-nn" }, { "text": "Reply to Shvaika et al.: Presence of a boson peak in anharmonic phonon\n models with Akhiezer-type damping: We reply to the Comment by Svhaika, Ruocco, Schirmacher and collaborators.\nThere were two accidental mistakes in our original paper (Phys. Rev. Lett. 112,\n145501 (2019)), which have been now corrected. All the physical conclusions and\nresults of the original paper, including the prediction of boson peak due to\nanharmonicity, remain valid in the corrected version.", "category": "cond-mat_dis-nn" }, { "text": "Analytical Approach to Noise Effects on Synchronization in a System of\n Coupled Excitable Elements: We report relationships between the effects of noise and applied constant\ncurrents on the behavior of a system of excitable elements. The analytical\napproach based on the nonlinear Fokker-Planck equation of a mean-field model\nallows us to study the effects of noise without approximations only by dealing\nwith deterministic nonlinear dynamics . We find the similarity, with respect to\nthe occurrence of oscillations involving subcritical Hopf bifurcations, between\nthe systems of an excitable element with applied constant currents and\nmean-field coupled excitable elements with noise.", "category": "cond-mat_dis-nn" }, { "text": "On the Nature of Localization in Ti doped Si: Intermediate band semiconductors hold the promise to significantly improve\nthe efficiency of solar cells, but only if the intermediate impurity band is\nmetallic. We apply a recently developed first principles method to investigate\nthe origin of electron localization in Ti doped Si, a promising candidate for\nintermediate band solar cells. Although Anderson localization is often\noverlooked in the context of intermediate band solar cells, our results show\nthat in Ti doped Si it plays a more important role in the metal insulator\ntransition than Mott localization. Implications for the theory of intermediate\nband solar cells are discussed.", "category": "cond-mat_dis-nn" }, { "text": "Inner Structure of Many-Body Localization Transition and Fulfillment of\n Harris Criterion: We treat disordered Heisenberg model in 1D as the \"standard model\" of\nmany-body localization (MBL). Two independent order parameters stemming purely\nfrom the half-chain von Neumann entanglement entropy $S_{\\textrm{vN}}$ are\nintroduced to probe its eigenstate transition. From symmetry-endowed entropy\ndecomposition, they are probability distribution deviation $|d(p_n)|$ and von\nNeumann entropy $S_{\\textrm{vN}}^{n}(D_n\\!=\\!\\mbox{max})$ of the\nmaximum-dimensional symmetry subdivision. Finite-size analyses reveal that\n$\\{p_n\\}$ drives the localization transition, preceded by a thermalization\nbreakdown transition governed by $\\{S_{\\textrm{vN}}^{n}\\}$. For noninteracting\ncase, these transitions coincide, but in interacting situation they separate.\nSuch separability creates an intermediate phase region and may help\ndiscriminate between the Anderson and MBL transitions. An obstacle whose\nsolution eludes community to date is the violation of Harris criterion in\nnearly all numeric investigations of MBL so far. Upon elucidating the mutually\nindependent components in $S_{\\textrm{vN}}$, it is clear that previous studies\nof eigenspectra, $S_{\\textrm{vN}}$, and the like lack resolution to pinpoint\n(thus completely overlook) the crucial internal structures of the transition.\nWe show, for the first time, that after this necessary decoupling, the\nuniversal critical exponents for both transitions of $|d(p_n)|$ and\n$S_{\\textrm{vN}}^{n}(D_n\\!=\\!\\mbox{max})$ fulfill the Harris criterion:\n$\\nu\\approx2.0\\ (\\nu\\approx1.5)$ for quench (quasirandom) disorder. Our work\nputs forth \"symmetry combined with entanglement\" as the missing organization\nprinciple for the generic eigenstate matter and transition.", "category": "cond-mat_dis-nn" }, { "text": "Generalized multifractality at the spin quantum Hall transition:\n Percolation mapping and pure-scaling observables: This work extends the analysis of the generalized multifractality of critical\neigenstates at the spin quantum Hall transition in two-dimensional disordered\nsuperconductors [J. F. Karcher et al, Annals of Physics, 435, 168584 (2021)]. A\nmapping to classical percolation is developed for a certain set of\ngeneralized-multifractality observables. In this way, exact analytical results\nfor the corresponding exponents are obtained. Furthermore, a general\nconstruction of positive pure-scaling eigenfunction observables is presented,\nwhich permits a very efficient numerical determination of scaling exponents. In\nparticular, all exponents corresponding to polynomial pure-scaling observables\nup to the order $q=5$ are found numerically. For the observables for which the\npercolation mapping is derived, analytical and numerical results are in perfect\nagreement with each other. The analytical and numerical results unambiguously\ndemonstrate that the generalized parabolicity (i.e., proportionality to\neigenvalues of the quadratic Casimir operator) does not hold for the spectrum\nof generalized-multifractality exponents. This excludes\nWess-Zumino-Novikov-Witten models, and, more generally, any theories with local\nconformal invariance, as candidates for the fixed-point theory of the spin\nquantum Hall transition. The observable construction developed in this work\npaves a way to investigation of generalized multifractality at\nAnderson-localization critical points of various symmetry classes.", "category": "cond-mat_dis-nn" }, { "text": "Random Dirac Fermions and Non-Hermitian Quantum Mechanics: We study the influence of a strong imaginary vector potential on the quantum\nmechanics of particles confined to a two-dimensional plane and propagating in a\nrandom impurity potential. We show that the wavefunctions of the non-Hermitian\noperator can be obtained as the solution to a two-dimensional Dirac equation in\nthe presence of a random gauge field. Consequences for the localization\nproperties and the critical nature of the states are discussed.", "category": "cond-mat_dis-nn" }, { "text": "Effect of coupling asymmetry on mean-field solutions of direct and\n inverse Sherrington-Kirkpatrick model: We study how the degree of symmetry in the couplings influences the\nperformance of three mean field methods used for solving the direct and inverse\nproblems for generalized Sherrington-Kirkpatrick models. In this context, the\ndirect problem is predicting the potentially time-varying magnetizations. The\nthree theories include the first and second order Plefka expansions, referred\nto as naive mean field (nMF) and TAP, respectively, and a mean field theory\nwhich is exact for fully asymmetric couplings. We call the last of these simply\nMF theory. We show that for the direct problem, nMF performs worse than the\nother two approximations, TAP outperforms MF when the coupling matrix is nearly\nsymmetric, while MF works better when it is strongly asymmetric. For the\ninverse problem, MF performs better than both TAP and nMF, although an ad hoc\nadjustment of TAP can make it comparable to MF. For high temperatures the\nperformance of TAP and MF approach each other.", "category": "cond-mat_dis-nn" }, { "text": "Flat band states: disorder and nonlinearity: We study the critical behaviour of Anderson localized modes near intersecting\nflat and dispersive bands in the quasi-one-dimensional diamond ladder with weak\ndiagonal disorder $W$. The localization length $\\xi$ of the flat band states\nscales with disorder as $\\xi \\sim W^{-\\gamma}$, with $\\gamma \\approx 1.3$, in\ncontrast to the dispersive bands with $\\gamma =2$. A small fraction of\ndispersive modes mixed with the flat band states is responsible for the unusual\nscaling. Anderson localization is therefore controlled by two different length\nscales. Nonlinearity can produce qualitatively different wave spreading\nregimes, from enhanced expansion to resonant tunneling and self-trapping.", "category": "cond-mat_dis-nn" }, { "text": "Transition from localized to mean field behaviour of cascading failures\n in the fiber bundle model on complex networks: We study the failure process of fiber bundles on complex networks focusing on\nthe effect of the degree of disorder of fibers' strength on the transition from\nlocalized to mean field behaviour. Starting from a regular square lattice we\napply the Watts-Strogatz rewiring technique to introduce long range random\nconnections in the load transmission network and analyze how the ultimate\nstrength of the bundle and the statistics of the size of failure cascades\nchange when the rewiring probability is gradually increased. Our calculations\nrevealed that the degree of strength disorder of nodes of the network has a\nsubstantial effect on the localized to mean field transition. In particular, we\nshow that the transition sets on at a finite value of the rewiring probability,\nwhich shifts to higher values as the degree of disorder is reduced. The\ntransition is limited to a well defined range of disorder, so that there exists\na threshold disorder of nodes' strength below which the randomization of the\nnetwork structure does not provide any improvement neither of the overall load\nbearing capacity nor of the cascade tolerance of the system. At low strength\ndisorder the fully random network is the most stable one, while at high\ndisorder best cascade tolerance is obtained at a lower structural randomness.\nBased on the interplay of the network structure and strength disorder we\nconstruct an analytical argument which provides a reasonable description of the\nnumerical findings.", "category": "cond-mat_dis-nn" }, { "text": "Anderson Localization on the Bethe Lattice using Cages and the Wegner\n Flow: Anderson localization on tree-like graphs such as the Bethe lattice, Cayley\ntree, or random regular graphs has attracted attention due to its apparent\nmathematical tractability, hypothesized connections to many-body localization,\nand the possibility of non-ergodic extended regimes. This behavior has been\nconjectured to also appear in many-body localization as a \"bad metal\" phase,\nand constitutes an intermediate possibility between the extremes of ergodic\nquantum chaos and integrable localization. Despite decades of research, a\ncomplete consensus understanding of this model remains elusive. Here, we use\ncages, maximally tree-like structures from extremal graph theory; and numerical\ncontinuous unitary Wegner flows of the Anderson Hamiltonian to develop an\nintuitive picture which, after extrapolating to the infinite Bethe lattice,\nappears to capture ergodic, non-ergodic extended, and fully localized behavior.", "category": "cond-mat_dis-nn" }, { "text": "Spurious self-feedback of mean-field predictions inflates infection\n curves: The susceptible-infected-recovered (SIR) model and its variants form the\nfoundation of our understanding of the spread of diseases. Here, each agent can\nbe in one of three states (susceptible, infected, or recovered), and\ntransitions between these states follow a stochastic process. The probability\nof an agent becoming infected depends on the number of its infected neighbors,\nhence all agents are correlated. A common mean-field theory of the same\nstochastic process however, assumes that the agents are statistically\nindependent. This leads to a self-feedback effect in the approximation: when an\nagent infects its neighbors, this infection may subsequently travel back to the\noriginal agent at a later time, leading to a self-infection of the agent which\nis not present in the underlying stochastic process. We here compute the first\norder correction to the mean-field assumption, which takes fluctuations up to\nsecond order in the interaction strength into account. We find that it cancels\nthe self-feedback effect, leading to smaller infection rates. In the SIR model\nand in the SIRS model, the correction significantly improves predictions. In\nparticular, it captures how sparsity dampens the spread of the disease: this\nindicates that reducing the number of contacts is more effective than predicted\nby mean-field models.", "category": "cond-mat_dis-nn" }, { "text": "Critical synchronization dynamics of the Kuramoto model on connectome\n and small world graphs: The hypothesis, that cortical dynamics operates near criticality also\nsuggests, that it exhibits universal critical exponents which marks the\nKuramoto equation, a fundamental model for synchronization, as a prime\ncandidate for an underlying universal model. Here, we determined the\nsynchronization behavior of this model by solving it numerically on a large,\nweighted human connectome network, containing 804092 nodes, in an assumed\nhomeostatic state. Since this graph has a topological dimension $d < 4$, a real\nsynchronization phase transition is not possible in the thermodynamic limit,\nstill we could locate a transition between partially synchronized and\ndesynchronized states. At this crossover point we observe power-law--tailed\nsynchronization durations, with $\\tau_t \\simeq 1.2(1)$, away from experimental\nvalues for the brain. For comparison, on a large two-dimensional lattice,\nhaving additional random, long-range links, we obtain a mean-field value:\n$\\tau_t \\simeq 1.6(1)$. However, below the transition of the connectome we\nfound global coupling control-parameter dependent exponents $1 < \\tau_t \\le 2$,\noverlapping with the range of human brain experiments. We also studied the\neffects of random flipping of a small portion of link weights, mimicking a\nnetwork with inhibitory interactions, and found similar results. The\ncontrol-parameter dependent exponent suggests extended dynamical criticality\nbelow the transition point.", "category": "cond-mat_dis-nn" }, { "text": "Critical Percolation Without Fine Tuning on the Surface of a Topological\n Superconductor: We present numerical evidence that most two-dimensional surface states of a\nbulk topological superconductor (TSC) sit at an integer quantum Hall plateau\ntransition. We study TSC surface states in class CI with quenched disorder.\nLow-energy (finite-energy) surface states were expected to be critically\ndelocalized (Anderson localized). We confirm the low-energy picture, but find\ninstead that finite-energy states are also delocalized, with universal\nstatistics that are independent of the TSC winding number, and consistent with\nthe spin quantum Hall plateau transition (percolation).", "category": "cond-mat_dis-nn" }, { "text": "The number of matchings in random graphs: We study matchings on sparse random graphs by means of the cavity method. We\nfirst show how the method reproduces several known results about maximum and\nperfect matchings in regular and Erdos-Renyi random graphs. Our main new result\nis the computation of the entropy, i.e. the leading order of the logarithm of\nthe number of solutions, of matchings with a given size. We derive both an\nalgorithm to compute this entropy for an arbitrary graph with a girth that\ndiverges in the large size limit, and an analytic result for the entropy in\nregular and Erdos-Renyi random graph ensembles.", "category": "cond-mat_dis-nn" }, { "text": "Non-trivial fixed point structure of the two-dimensional +-J 3-state\n Potts ferromagnet/spin glass: The fixed point structure of the 2D 3-state random-bond Potts model with a\nbimodal ($\\pm$J) distribution of couplings is for the first time fully\ndetermined using numerical renormalization group techniques. Apart from the\npure and T=0 critical fixed points, two other non-trivial fixed points are\nfound. One is the critical fixed point for the random-bond, but unfrustrated,\nferromagnet. The other is a bicritical fixed point analogous to the bicritical\nNishimori fixed point found in the random-bond frustrated Ising model.\nEstimates of the associated critical exponents are given for the various fixed\npoints of the random-bond Potts model.", "category": "cond-mat_dis-nn" }, { "text": "Retrieval and Chaos in Extremely Diluted Non-Monotonic Neural Networks: We discuss, in this paper, the dynamical properties of extremely diluted,\nnon-monotonic neural networks. Assuming parallel updating and the Hebb\nprescription for the synaptic connections, a flow equation for the macroscopic\noverlap is derived. A rich dynamical phase diagram was obtained, showing a\nstable retrieval phase, as well as a cycle two and chaotic behavior. Numerical\nsimulations were performed, showing good agreement with analytical results.\nFurthermore, the simulations give an additional insight into the microscopic\ndynamical behavior during the chaotic phase. It is shown that the freezing of\nindividual neuron states is related to the structure of chaotic attractors.", "category": "cond-mat_dis-nn" }, { "text": "Spin glass induced by infinitesimal disorder in geometrically frustrated\n kagome lattice: We propose a method to study the magnetic properties of a disordered Ising\nkagome lattice. The model considers small spin clusters with infinite-range\ndisordered couplings and short-range ferromagnetic (FE) or antiferromagnetic\ninteractions. The correlated cluster mean-field theory is used to obtain an\neffective single-cluster problem. A finite disorder intensity in FE kagome\nlattice introduces a cluster spin-glass (CSG) phase. Nevertheless, an\ninfinitesimal disorder stabilizes the CSG behavior in the geometrically\nfrustrated kagome system. Entropy, magnetic susceptibility and spin-spin\ncorrelation are used to describe the interplay between disorder and geometric\nfrustration (GF). We find that GF plays an important role in the low-disorder\nCSG phase. However, the increase of disorder can rule out the effect of GF.", "category": "cond-mat_dis-nn" }, { "text": "Wave Transport in disordered waveguides: closed channel contributions\n and the coherent and diffuse fields: We study the wave transport through a disordered system inside a waveguide.\nThe expectation value of the complex reflection and transmission coefficients\n(the coherent fields) as well as the transmittance and reflectance are obtained\nnumerically. The numerical results show that the averages of the coherent\nfields are only relevant for direct processes, while the transmittance and\nreflectance are mainly dominated by the diffuse intensities, which come from\nthe statistical fluctuations of the fields.", "category": "cond-mat_dis-nn" }, { "text": "How to predict critical state: Invariance of Lyapunov exponent in dual\n spaces: The critical state in disordered systems, a fascinating and subtle\neigenstate, has attracted a lot of research interest. However, the nature of\nthe critical state is difficult to describe quantitatively. Most of the studies\nfocus on numerical verification, and cannot predict the system in which the\ncritical state exists. In this work, we propose an explicit and universal\ncriterion that for the critical state Lyapunov exponent should be 0\nsimultaneously in dual spaces, namely Lyapunov exponent remains invariant under\nFourier transform. With this criterion, we exactly predict a specific system\nhosting a large number of critical states for the first time. Then, we perform\nnumerical verification of the theoretical prediction, and display the\nself-similarity and scale invariance of the critical state. Finally, we\nconjecture that there exist some kind of connection between the invariance of\nthe Lyapunov exponent and conformal invariance.", "category": "cond-mat_dis-nn" }, { "text": "Stability of networks of delay-coupled delay oscillators: Dynamical networks with time delays can pose a considerable challenge for\nmathematical analysis. Here, we extend the approach of generalized modeling to\ninvestigate the stability of large networks of delay-coupled delay oscillators.\nWhen the local dynamical stability of the network is plotted as a function of\nthe two delays then a pattern of tongues is revealed. Exploiting a link between\nstructure and dynamics, we identify conditions under which perturbations of the\ntopology have a strong impact on the stability. If these critical regions are\navoided the local stability of large random networks can be well approximated\nanalytically.", "category": "cond-mat_dis-nn" }, { "text": "Evidence for the double degeneracy of the ground-state in the 3D $\\pm J$\n spin glass: A bivariate version of the multicanonical Monte Carlo method and its\napplication to the simulation of the three-dimensional $\\pm J$ Ising spin glass\nare described. We found the autocorrelation time associated with this\nparticular multicanonical method was approximately proportional to the system\nvolume, which is a great improvement over previous methods applied to\nspin-glass simulations. The principal advantage of this version of the\nmulticanonical method, however, was its ability to access information\npredictive of low-temperature behavior. At low temperatures we found results on\nthe three-dimensional $\\pm J$ Ising spin glass consistent with a double\ndegeneracy of the ground-state: the order-parameter distribution function\n$P(q)$ converged to two delta-function peaks and the Binder parameter\napproached unity as the system size was increased. With the same density of\nstates used to compute these properties at low temperature, we found their\nbehavior changing as the temperature is increased towards the spin glass\ntransition temperature. Just below this temperature, the behavior is consistent\nwith the standard mean-field picture that has an infinitely degenerate ground\nstate. Using the concept of zero-energy droplets, we also discuss the structure\nof the ground-state degeneracy. The size distribution of the zero-energy\ndroplets was found to produce the two delta-function peaks of $P(q)$.", "category": "cond-mat_dis-nn" }, { "text": "Comment on \"Collective modes and gapped momentum states in liquid Ga:\n Experiment, theory, and simulation\": We show that the presented in Phys.Rev.B, v.101, 214312 (2020) theoretical\nexpressions for longitudinal current spectral function $C^L(k,\\omega)$ and\ndispersion of collective excitations are not correct. Indeed, they are not\ncompatible with the continuum limit and $C^L(k,\\omega\\to 0)$ contradicts the\ncontinuity equation.", "category": "cond-mat_dis-nn" }, { "text": "Finite-time Singularities in Surface-Diffusion Instabilities are Cured\n by Plasticity: A free material surface which supports surface diffusion becomes unstable\nwhen put under external non-hydrostatic stress. Since the chemical potential on\na stressed surface is larger inside an indentation, small shape fluctuations\ndevelop because material preferentially diffuses out of indentations. When the\nbulk of the material is purely elastic one expects this instability to run into\na finite-time cusp singularity. It is shown here that this singularity is cured\nby plastic effects in the material, turning the singular solution to a regular\ncrack.", "category": "cond-mat_dis-nn" }, { "text": "Transport of multiple users in complex networks: We study the transport properties of model networks such as scale-free and\nErd\\H{o}s-R\\'{e}nyi networks as well as a real network. We consider the\nconductance $G$ between two arbitrarily chosen nodes where each link has the\nsame unit resistance. Our theoretical analysis for scale-free networks predicts\na broad range of values of $G$, with a power-law tail distribution $\\Phi_{\\rm\nSF}(G)\\sim G^{-g_G}$, where $g_G=2\\lambda -1$, and $\\lambda$ is the decay\nexponent for the scale-free network degree distribution. We confirm our\npredictions by large scale simulations. The power-law tail in $\\Phi_{\\rm\nSF}(G)$ leads to large values of $G$, thereby significantly improving the\ntransport in scale-free networks, compared to Erd\\H{o}s-R\\'{e}nyi networks\nwhere the tail of the conductivity distribution decays exponentially. We\ndevelop a simple physical picture of the transport to account for the results.\nWe study another model for transport, the \\emph{max-flow} model, where\nconductance is defined as the number of link-independent paths between the two\nnodes, and find that a similar picture holds. The effects of distance on the\nvalue of conductance are considered for both models, and some differences\nemerge. We then extend our study to the case of multiple sources, where the\ntransport is define between two \\emph{groups} of nodes. We find a fundamental\ndifference between the two forms of flow when considering the quality of the\ntransport with respect to the number of sources, and find an optimal number of\nsources, or users, for the max-flow case. A qualitative (and partially\nquantitative) explanation is also given.", "category": "cond-mat_dis-nn" }, { "text": "Stability of critical behaviour of weakly disordered systems with\n respect to the replica symmetry breaking: A field-theoretic description of the critical behaviour of the weakly\ndisordered systems is given. Directly, for three- and two-dimensional systems a\nrenormalization analysis of the effective Hamiltonian of model with replica\nsymmetry breaking (RSB) potentials is carried out in the two-loop\napproximation. For case with 1-step RSB the fixed points (FP's) corresponding\nto stability of the various types of critical behaviour are identified with the\nuse of the Pade-Borel summation technique. Analysis of FP's has shown a\nstability of the critical behaviour of the weakly disordered systems with\nrespect to RSB effects and realization of former scenario of disorder influence\non critical behaviour.", "category": "cond-mat_dis-nn" }, { "text": "Phase transitions induced by microscopic disorder: a study based on the\n order parameter expansion: Based on the order parameter expansion, we present an approximate method\nwhich allows us to reduce large systems of coupled differential equations with\ndiverse parameters to three equations: one for the global, mean field, variable\nand two which describe the fluctuations around this mean value. With this tool\nwe analyze phase-transitions induced by microscopic disorder in three\nprototypical models of phase-transitions which have been studied previously in\nthe presence of thermal noise. We study how macroscopic order is induced or\ndestroyed by time independent local disorder and analyze the limits of the\napproximation by comparing the results with the numerical solutions of the\nself-consistency equation which arises from the property of self-averaging.\nFinally, we carry on a finite-size analysis of the numerical results and\ncalculate the corresponding critical exponents.", "category": "cond-mat_dis-nn" }, { "text": "Observation of infinite-range intensity correlations above, at and below\n the 3D Anderson localization transition: We investigate long-range intensity correlations on both sides of the\nAnderson transition of classical waves in a three-dimensional (3D) disordered\nmaterial. Our ultrasonic experiments are designed to unambiguously detect a\nrecently predicted infinite-range C0 contribution, due to local density of\nstates fluctuations near the source. We find that these C0 correlations, in\naddition to C2 and C3 contributions, are significantly enhanced near mobility\nedges. Separate measurements of the inverse participation ratio reveal a link\nbetween C0 and the anomalous dimension \\Delta_2, implying that C0 may also be\nused to explore the critical regime of the Anderson transition.", "category": "cond-mat_dis-nn" }, { "text": "Challenges and opportunities in the supervised learning of quantum\n circuit outputs: Recently, deep neural networks have proven capable of predicting some output\nproperties of relevant random quantum circuits, indicating a strategy to\nemulate quantum computers alternative to direct simulation methods such as,\ne.g., tensor-network methods. However, the reach of this alternative strategy\nis not yet clear. Here we investigate if and to what extent neural networks can\nlearn to predict the output expectation values of circuits often employed in\nvariational quantum algorithms, namely, circuits formed by layers of CNOT gates\nalternated with random single-qubit rotations. On the one hand, we find that\nthe computational cost of supervised learning scales exponentially with the\ninter-layer variance of the random angles. This allows entering a regime where\nquantum computers can easily outperform classical neural networks. On the other\nhand, circuits featuring only inter-qubit angle variations are easily emulated.\nIn fact, thanks to a suitable scalable design, neural networks accurately\npredict the output of larger and deeper circuits than those used for training,\neven reaching circuit sizes which turn out to be intractable for the most\ncommon simulation libraries, considering both state-vector and tensor-network\nalgorithms. We provide a repository of testing data in this regime, to be used\nfor future benchmarking of quantum devices and novel classical algorithms.", "category": "cond-mat_dis-nn" }, { "text": "Stability of a neural network model with small-world connections: Small-world networks are highly clustered networks with small distances among\nthe nodes. There are many biological neural networks that present this kind of\nconnections. There are no special weightings in the connections of most\nexisting small-world network models. However, this kind of simply-connected\nmodels cannot characterize biological neural networks, in which there are\ndifferent weights in synaptic connections. In this paper, we present a neural\nnetwork model with weighted small-world connections, and further investigate\nthe stability of this model.", "category": "cond-mat_dis-nn" }, { "text": "Numerical Simulations of Random Phase Sine-Gordon Model and\n Renormalization Group Predictions: Numerical Simulations of the random phase sine-Gordon model suffer from\nstrong finite size effects preventing the non-Gaussian $\\log^2 r$ component of\nthe spatial correlator from following the universal infinite volume prediction.\nWe show that a finite size prediction based on perturbative Renormalisation\nGroup (RG) arguments agrees well with new high precision simulations for small\ncoupling and close to the critical temperature.", "category": "cond-mat_dis-nn" }, { "text": "Localization properties of the sparse Barrat-M\u00e9zard trap model: Inspired by works on the Anderson model on sparse graphs, we devise a method\nto analyze the localization properties of sparse systems that may be solved\nusing cavity theory. We apply this method to study the properties of the\neigenvectors of the master operator of the sparse Barrat-M\\'ezard trap model,\nwith an emphasis on the extended phase. As probes for localization, we consider\nthe inverse participation ratio and the correlation volume, both dependent on\nthe distribution of the diagonal elements of the resolvent. Our results reveal\na rich and non-trivial behavior of the estimators across the spectrum of\nrelaxation rates and an interplay between entropic and activation mechanisms of\nrelaxation that give rise to localized modes embedded in the bulk of extended\nstates. We characterize this route to localization and find it to be distinct\nfrom the paradigmatic Anderson model or standard random matrix systems.", "category": "cond-mat_dis-nn" }, { "text": "A dedicated algorithm for calculating ground states for the triangular\n random bond Ising model: In the presented article we present an algorithm for the computation of\nground state spin configurations for the 2d random bond Ising model on planar\ntriangular lattice graphs. Therefore, it is explained how the respective ground\nstate problem can be mapped to an auxiliary minimum-weight perfect matching\nproblem, solvable in polynomial time. Consequently, the ground state properties\nas well as minimum-energy domain wall (MEDW) excitations for very large 2d\nsystems, e.g. lattice graphs with up to N=384x384 spins, can be analyzed very\nfast. Here, we investigate the critical behavior of the corresponding T=0\nferromagnet to spin-glass transition, signaled by a breakdown of the\nmagnetization, using finite-size scaling analyses of the magnetization and MEDW\nexcitation energy and we contrast our numerical results with previous\nsimulations and presumably exact results.", "category": "cond-mat_dis-nn" }, { "text": "Distribution of shortest cycle lengths in random networks: We present analytical results for the distribution of shortest cycle lengths\n(DSCL) in random networks. The approach is based on the relation between the\nDSCL and the distribution of shortest path lengths (DSPL). We apply this\napproach to configuration model networks, for which analytical results for the\nDSPL were obtained before. We first calculate the fraction of nodes in the\nnetwork which reside on at least one cycle. Conditioning on being on a cycle,\nwe provide the DSCL over ensembles of configuration model networks with degree\ndistributions which follow a Poisson distribution (Erdos-R\\'enyi network),\ndegenerate distribution (random regular graph) and a power-law distribution\n(scale-free network). The mean and variance of the DSCL are calculated. The\nanalytical results are found to be in very good agreement with the results of\ncomputer simulations.", "category": "cond-mat_dis-nn" }, { "text": "Low Temperature Behavior of the Thermopower in Disordered Systems near\n the Anderson Transition: We investigate the behavior of the thermoelectric power [S] in disordered\nsystems close to the Anderson-type metal-insulator transition [MIT] at low\ntemperatures. In the literature, we find contradictory results for S. It is\neither argued to diverge or to remain a constant as the MIT is approached. To\nresolve this dilemma, we calculate the number density of electrons at the MIT\nin disordered systems using an averaged density of states obtained by\ndiagonalizing the three-dimensional Anderson model of localization. From the\nnumber density we obtain the temperature dependence of the chemical potential\nnecessary to solve for S. Without any additional approximation, we use the\nChester-Thellung-Kubo-Greenwood formulation and numerically obtain the behavior\nof S at low T as the Anderson transition is approached from the metallic side.\nWe show that indeed S does not diverge.", "category": "cond-mat_dis-nn" }, { "text": "Chemical potential in disordered organic materials: Charge carrier mobility in disordered organic materials is being actively\nstudied, motivated by several applications such as organic light emitting\ndiodes and organic field-effect transistors. It is known that the mobility in\ndisordered organic materials depends on the chemical potential which in turn\ndepends on the carrier concentration. However, the functional dependence of\nchemical potential on the carrier concentration is not known. In this study, we\nfocus on the chemical potential in organic materials with Gaussian disorder. We\nidentify three cases of non-degenerate, degenerate and saturated regimes. In\neach regime we calculate analytically the chemical potential as a function of\nthe carrier concentration and the energetic disorder from the first principles.", "category": "cond-mat_dis-nn" }, { "text": "The perturbative structure of spin glass field theory: Cubic replicated field theory is used to study the glassy phase of the\nshort-range Ising spin glass just below the transition temperature, and for\nsystems above, at, and slightly below the upper critical dimension six. The\norder parameter function is computed up to two-loop order. There are two,\nwell-separated bands in the mass spectrum, just as in mean field theory. The\nsmall mass band acts as an infrared cutoff, whereas contributions from the\nlarge mass region can be computed perturbatively (d>6), or interpreted by the\nepsilon-expansion around the critical fixed point (d=6-epsilon). The one-loop\ncalculation of the (momentum-dependent) longitudinal mass, and the whole\nreplicon sector is also presented. The innocuous behavior of the replicon\nmasses while crossing the upper critical dimension shows that the ultrametric\nreplica symmetry broken phase remains stable below six dimensions.", "category": "cond-mat_dis-nn" }, { "text": "A FDR-preserving field theory for interacting Brownian particles:\n one-loop theory and MCT: We develop a field theoretical treatment of a model of interacting Brownian\nparticles. We pay particular attention to the requirement of the time reversal\ninvariance and the fluctuation-dissipation relationship (FDR). The method used\nis a modified version of the auxiliary field method due originally to\nAndreanov, Biroli and Lefevre [J. Stat. Mech. P07008 (2006)]. We recover the\ncorrect diffusion law when the interaction is dropped as well as the standard\nmode coupling equation in the one-loop order calculation for interacting\nBrownian particle systems.", "category": "cond-mat_dis-nn" }, { "text": "On calculation of effective conductivity of inhomogeneous metals: In the framework of the perturbation theory an expression suitable for\ncalculation of the effective conductivity of 3-D inhomogeneous metals is\nderived. Formally, the final expression is an exact result, however, a function\nwritten as a perturbation series enters the answer. More accurately, when\nstatistical properties of the given inhomogeneous medium are known, our result\nprovides the regular algorithm for calculation of the effective conductivity up\nto an arbitrary term of the perturbation series. As examples, we examine (i) an\nisotropic metal whose local conductivity is a Gaussianly distributed random\nfunction, (ii) the effective conductivity of polycrystalline metals.", "category": "cond-mat_dis-nn" }, { "text": "Comment on \"Failure of the simultaneous block diagonalization technique\n applied to complete and cluster synchronization of random networks\": In their recent preprint [arXiv:2108.07893v1], S. Panahi, N. Amaya, I.\nKlickstein, G. Novello, and F. Sorrentino tested the simultaneous block\ndiagonalization (SBD) technique on synchronization in random networks and found\nthe dimensionality reduction to be limited. Based on this observation, they\nclaimed the SBD technique to be a failure in generic situations. Here, we show\nthat this is not a failure of the SBD technique. Rather, it is caused by\ninappropriate choices of network models. SBD provides a unified framework to\nanalyze the stability of synchronization patterns that are not encumbered by\nsymmetry considerations, and it always finds the optimal reduction for any\ngiven synchronization pattern and network structure [SIAM Rev. 62, 817-836\n(2020)]. The networks considered by Panahi et al. are poor benchmarks for the\nperformance of the SBD technique, as these systems are often intrinsically\nirreducible, regardless of the method used. Thus, although the results in\nPanahi et al. are technically valid, their interpretations are misleading and\nakin to claiming a community detection algorithm to be a failure because it\ndoes not find any meaningful communities in Erd\\H{o}s-R\\'enyi networks.", "category": "cond-mat_dis-nn" }, { "text": "Molecular dynamics simulation of aging in amorphous silica: By means of molecular dynamics simulations we examine the aging process of a\nstrong glass former, a silica melt modeled by the BKS potential. The system is\nquenched from a temperature above to one below the critical temperature, and\nthe potential energy and the scattering function C(t_w,t+t_w) for various\nwaiting times t_w after the quench are measured. We find that both\nqualitatively and quantitatively the results agree well with the ones found in\nsimilar simulations of a fragile glass former, a Lennard-Jones liquid.", "category": "cond-mat_dis-nn" }, { "text": "Critical dynamics on a large human Open Connectome network: Extended numerical simulations of threshold models have been performed on a\nhuman brain network with N=836733 connected nodes available from the Open\nConnectome project. While in case of simple threshold models a sharp\ndiscontinuous phase transition without any critical dynamics arises, variable\nthresholds models exhibit extended power-law scaling regions. This is\nattributed to fact that Griffiths effects, stemming from the\ntopological/interaction heterogeneity of the network, can become relevant if\nthe input sensitivity of nodes is equalized. I have studied the effects effects\nof link directness, as well as the consequence of inhibitory connections.\nNon-universal power-law avalanche size and time distributions have been found\nwith exponents agreeing with the values obtained in electrode experiments of\nthe human brain. The dynamical critical region occurs in an extended control\nparameter space without the assumption of self organized criticality.", "category": "cond-mat_dis-nn" }, { "text": "Classical Representation of the 1D Anderson Model: A new approach is applied to the 1D Anderson model by making use of a\ntwo-dimensional Hamiltonian map. For a weak disorder this approach allows for a\nsimple derivation of correct expressions for the localization length both at\nthe center and at the edge of the energy band, where standard perturbation\ntheory fails. Approximate analytical expressions for strong disorder are also\nobtained.", "category": "cond-mat_dis-nn" }, { "text": "Comment on \"Critical point scaling of Ising spin glasses in a magnetic\n field\" by J. Yeo and M.A. Moore: In a section of a recent publication, [J. Yeo and M.A. Moore, Phys. Rev. B\n91, 104432 (2015)], the authors discuss some of the arguments in the paper by\nParisi and Temesv\\'ari [Nuclear Physics B 858, 293 (2012)]. In this comment, it\nis shown how these arguments are misinterpreted, and the existence of the\nAlmeida-Thouless transition in the upper critical dimension 6 reasserted.", "category": "cond-mat_dis-nn" }, { "text": "The Anderson transition: time reversal symmetry and universality: We report a finite size scaling study of the Anderson transition. Different\nscaling functions and different values for the critical exponent have been\nfound, consistent with the existence of the orthogonal and unitary universality\nclasses which occur in the field theory description of the transition. The\ncritical conductance distribution at the Anderson transition has also been\ninvestigated and different distributions for the orthogonal and unitary classes\nobtained.", "category": "cond-mat_dis-nn" }, { "text": "Pure scaling operators at the integer quantum Hall plateau transition: Stationary wave functions at the transition between plateaus of the integer\nquantum Hall effect are known to exhibit multi-fractal statistics. Here we\nexplore this critical behavior for the case of scattering states of the\nChalker-Coddington model with point contacts. We argue that moments formed from\nthe wave amplitudes of critical scattering states decay as pure powers of the\ndistance between the points of contact and observation. These moments in the\ncontinuum limit are proposed to be correlations functions of primary fields of\nan underlying conformal field theory. We check this proposal numerically by\nfinite-size scaling. We also verify the CFT prediction for a 3-point function\ninvolving two primary fields.", "category": "cond-mat_dis-nn" }, { "text": "Field theory for amorphous solids: Glasses at low temperature fluctuate around their inherent states; glassy\nanomalies reflect the structure of these states. Recently there have been\nnumerous observations of long-range stress correlations in glassy materials,\nfrom supercooled liquids to colloids and granular materials, but without a\ncommon explanation. Herein it is shown, using a field theory of inherent\nstates, that long-range stress correlations follow from mechanical equilibrium\nalone, with explicit predictions for stress correlations in 2 and 3 dimensions.\n`Equations of state' relating fluctuations to imposed stresses are derived, as\nwell as field equations that fix the spatial structure of stresses in arbitrary\ngeometries. Finally, a new holographic quantity in 3D amorphous systems is\nidentified.", "category": "cond-mat_dis-nn" }, { "text": "Metallic phase of disordered graphene superlattices with long-range\n correlations: Using the transfer matrix method, we study the conductance of the chiral\nparticles through a monolayer graphene superlattice with long-range correlated\ndisorder distributed on the potential of the barriers. Even though the\ntransmission of the particles through graphene superlattice with white noise\npotentials is suppressed, the transmission is revived in a wide range of angles\nwhen the potential heights are long-range correlated with a power spectrum\n$S(k)\\sim1/k^{\\beta}$. As a result, the conductance increases with increasing\nthe correlation exponent values gives rise a metallic phase. We obtain a phase\ntransition diagram in which a critical correlation exponent depends strongly on\ndisorder strength and slightly on the energy of the incident particles. The\nphase transition, on the other hand, appears in all ranges of the energy from\npropagating to evanescent mode regimes.", "category": "cond-mat_dis-nn" }, { "text": "Well-mixed Lotka-Volterra model with random strongly competitive\n interactions: The random Lotka-Volterra model is widely used to describe the dynamical and\nthermodynamic features of ecological communities. In this work, we consider\nrandom symmetric interactions between species and analyze the strongly\ncompetitive interaction case. We investigate different scalings for the\ndistribution of the interactions with the number of species and try to bridge\nthe gap with previous works. Our results show two different behaviors for the\nmean abundance at zero and finite temperature respectively, with a continuous\ncrossover between the two. We confirm and extend previous results obtained for\nweak interactions: at zero temperature, even in the strong competitive\ninteraction limit, the system is in a multiple-equilibria phase, whereas at\nfinite temperature only a unique stable equilibrium can exist. Finally, we\nestablish the qualitative phase diagrams in both cases and compare the two\nspecies abundance distributions.", "category": "cond-mat_dis-nn" }, { "text": "Critical parameters for the disorder-induced metal-insulator transition\n in FCC and BCC lattices: We use a transfer-matrix method to study the disorder-induced metal-insulator\ntransition. We take isotropic nearest- neighbor hopping and an onsite potential\nwith uniformly distributed disorder. Following previous work done on the simple\ncubic lattice, we perform numerical calculations for the body centered cubic\nand face centered cubic lattices, which are more common in nature. We obtain\nthe localization length from calculated Lyapunov exponents for different system\nsizes. This data is analyzed using finite-size scaling to find the critical\nparameters. We create an energy-disorder phase diagram for both lattice types,\nnoting that it is symmetric about the band center for the body centered cubic\nlattice, but not for the face centered cubic lattice. We find a critical\nexponent of approximately 1.5-1.6 for both lattice types for transitions\noccurring either at fixed energy or at fixed disorder, agreeing with results\npreviously obtained for other systems belonging to the same orthogonal\nuniversality class. We notice an increase in critical disorder with the number\nof nearest neighbors, which agrees with intuition.", "category": "cond-mat_dis-nn" }, { "text": "Optimal fluctuation approach to a directed polymer in a random medium: A modification of the optimal fluctuation approach is applied to study the\ntails of the free energy distribution function P(F) for an elastic string in\nquenched disorder both in the regions of the universal behavior of P(F) and in\nthe regions of large fluctuations, where the behavior of P(F) is non-universal.\nThe difference between the two regimes is shown to consist in whether it is\nnecessary or not to take into account the renormalization of parameters by the\nfluctuations of disorder in the vicinity of the optimal fluctuation.", "category": "cond-mat_dis-nn" }, { "text": "Critical parameters for the disorder-induced metal-insulator transition\n in FCC and BCC lattices: We use a transfer-matrix method to study the disorder-induced metal-insulator\ntransition. We take isotropic nearest- neighbor hopping and an onsite potential\nwith uniformly distributed disorder. Following previous work done on the simple\ncubic lattice, we perform numerical calculations for the body centered cubic\nand face centered cubic lattices, which are more common in nature. We obtain\nthe localization length from calculated Lyapunov exponents for different system\nsizes. This data is analyzed using finite-size scaling to find the critical\nparameters. We create an energy-disorder phase diagram for both lattice types,\nnoting that it is symmetric about the band center for the body centered cubic\nlattice, but not for the face centered cubic lattice. We find a critical\nexponent of approximately 1.5-1.6 for both lattice types for transitions\noccurring either at fixed energy or at fixed disorder, agreeing with results\npreviously obtained for other systems belonging to the same orthogonal\nuniversality class. We notice an increase in critical disorder with the number\nof nearest neighbors, which agrees with intuition.", "category": "cond-mat_dis-nn" }, { "text": "Percolation theory applied to measures of fragmentation in social\n networks: We apply percolation theory to a recently proposed measure of fragmentation\n$F$ for social networks. The measure $F$ is defined as the ratio between the\nnumber of pairs of nodes that are not connected in the fragmented network after\nremoving a fraction $q$ of nodes and the total number of pairs in the original\nfully connected network. We compare $F$ with the traditional measure used in\npercolation theory, $P_{\\infty}$, the fraction of nodes in the largest cluster\nrelative to the total number of nodes. Using both analytical and numerical\nmethods from percolation, we study Erd\\H{o}s-R\\'{e}nyi (ER) and scale-free (SF)\nnetworks under various types of node removal strategies. The removal strategies\nare: random removal, high degree removal and high betweenness centrality\nremoval. We find that for a network obtained after removal (all strategies) of\na fraction $q$ of nodes above percolation threshold, $P_{\\infty}\\approx\n(1-F)^{1/2}$. For fixed $P_{\\infty}$ and close to percolation threshold\n($q=q_c$), we show that $1-F$ better reflects the actual fragmentation. Close\nto $q_c$, for a given $P_{\\infty}$, $1-F$ has a broad distribution and it is\nthus possible to improve the fragmentation of the network. We also study and\ncompare the fragmentation measure $F$ and the percolation measure $P_{\\infty}$\nfor a real social network of workplaces linked by the households of the\nemployees and find similar results.", "category": "cond-mat_dis-nn" }, { "text": "Correlated Domains in Spin Glasses: We study the 3D Edwards-Anderson spin glasses, by analyzing spin-spin\ncorrelation functions in thermalized spin configurations at low T on large\nlattices. We consider individual disorder samples and analyze connected\nclusters of very correlated sites: we analyze how the volume and the surface of\nthese clusters increases with the lattice size. We qualify the important\nexcitations of the system by checking how large they are, and we define a\ncorrelation length by measuring their gyration radius. We find that the\nclusters have a very dense interface, compatible with being space filling.", "category": "cond-mat_dis-nn" }, { "text": "Irreversible Opinion Spreading on Scale-Free Networks: We study the dynamical and critical behavior of a model for irreversible\nopinion spreading on Barab\\'asi-Albert (BA) scale-free networks by performing\nextensive Monte Carlo simulations. The opinion spreading within an\ninhomogeneous society is investigated by means of the magnetic Eden model, a\nnonequilibrium kinetic model for the growth of binary mixtures in contact with\na thermal bath. The deposition dynamics, which is studied as a function of the\ndegree of the occupied sites, shows evidence for the leading role played by\nhubs in the growth process. Systems of finite size grow either ordered or\ndisordered, depending on the temperature. By means of standard finite-size\nscaling procedures, the effective order-disorder phase transitions are found to\npersist in the thermodynamic limit. This critical behavior, however, is absent\nin related equilibrium spin systems such as the Ising model on BA scale-free\nnetworks, which in the thermodynamic limit only displays a ferromagnetic phase.\nThe dependence of these results on the degree exponent is also discussed for\nthe case of uncorrelated scale-free networks.", "category": "cond-mat_dis-nn" }, { "text": "Universal Sound Absorption in Amorphous Solids: A Theory of Elastically\n Coupled Generic Blocks: Glasses are known to exhibit quantitative universalities at low temperatures,\nthe most striking of which is the ultrasonic attenuation coefficient 1/Q. In\nthis work we develop a theory of coupled generic blocks with a certain\nrandomness property to show that universality emerges essentially due to the\ninteractions between elastic blocks, regardless of their microscopic nature.", "category": "cond-mat_dis-nn" }, { "text": "Speeding protein folding beyond the Go model: How a little frustration\n sometimes helps: Perturbing a Go model towards a realistic protein Hamiltonian by adding\nnon-native interactions, we find that the folding rate is in general enhanced\nas ruggedness is initially increased, as long as the protein is sufficiently\nlarge and flexible. Eventually the rate drops rapidly towards zero when\nruggedness significantly slows conformational transitions. Energy landscape\narguments for thermodynamics and kinetics are coupled with a treatment of\nnon-native collapse to elucidate this effect.", "category": "cond-mat_dis-nn" }, { "text": "Imaginary replica analysis of loopy regular random graphs: We present an analytical approach for describing spectrally constrained\nmaximum entropy ensembles of finitely connected regular loopy graphs, valid in\nthe regime of weak loop-loop interactions. We derive an expression for the\nleading two orders of the expected eigenvalue spectrum, through the use of\ninfinitely many replica indices taking imaginary values. We apply the method to\nmodels in which the spectral constraint reduces to a soft constraint on the\nnumber of triangles, which exhibit `shattering' transitions to phases with\nextensively many disconnected cliques, to models with controlled numbers of\ntriangles and squares, and to models where the spectral constraint reduces to a\ncount of the number of adjacency matrix eigenvalues in a given interval. Our\npredictions are supported by MCMC simulations based on edge swaps with\nnontrivial acceptance probabilities.", "category": "cond-mat_dis-nn" }, { "text": "Comparison of Gabay-Toulouse and de Almeida-Thouless instabilities for\n the spin glass XY model in a field on sparse random graphs: Vector spin glasses are known to show two different kinds of phase\ntransitions in presence of an external field: the so-called de Almeida-Thouless\nand Gabay-Toulouse lines. While the former has been studied to some extent on\nseveral topologies (fully connected, random graphs, finite-dimensional\nlattices, chains with long-range interactions), the latter has been studied\nonly in fully connected models, which however are known to show some unphysical\nbehaviors (e.g. the divergence of these critical lines in the zero-temperature\nlimit). Here we compute analytically both these critical lines for XY spin\nglasses on random regular graphs. We discuss the different nature of these\nphase transitions and the dependence of the critical behavior on the field\ndistribution. We also study the crossover between the two different critical\nbehaviors, by suitably tuning the field distribution.", "category": "cond-mat_dis-nn" }, { "text": "Distribution of the delay time and the dwell time for wave reflection\n from a long random potential: We re-examine and correct an earlier derivation of the distribution of the\nWigner phase delay time for wave reflection from a long one-dimensional\ndisordered conductor treated in the continuum limit. We then numerically\ncompare the distributions of the Wigner phase delay time and the dwell time,\nthe latter being obtained by the use of an infinitesimal imaginary potential as\na clock, and investigate the effects of strong disorder and a periodic\n(discrete) lattice background. We find that the two distributions coincide even\nfor strong disorder, but only for energies well away from the band-edges.", "category": "cond-mat_dis-nn" }, { "text": "Raman Scattering Due to Disorder-Induced Polaritons: The selection rules for dipole and Raman activity can be relaxed due to local\ndistortion of a crystalline structure. In this situation a dipole-inactive mode\ncan become simultaneously active in Raman scattering and in dipole interaction\nwith the electromagnetic field. The later interaction results in\ndisorder-induced polaritons, which could be observed in first-order Raman\nspectra. We calculate scattering cross-section in the case of a material with a\ndiamond-like average structure, and show that there exist a strong possibility\nof observing the disorder induced polaritons.", "category": "cond-mat_dis-nn" }, { "text": "Some Exact Results on the Ultrametric Overlap Distribution in Mean Field\n Spin Glass Models (I): The mean field spin glass model is analyzed by a combination of\nmathematically rigororous methods and a powerful Ansatz. The method exploited\nis general, and can be applied to others disordered mean field models such as,\ne.g., neural networks.\n It is well known that the probability measure of overlaps among replicas\ncarries the whole physical content of these models. A functional order\nparameter of Parisi type is introduced by rigorous methods, according to\nprevious works by F. Guerra. By the Ansatz that the functional order parameter\nis the correct order parameter of the model, we explicitly find the full\noverlap distribution. The physical interpretation of the functional order\nparameter is obtained, and ultrametricity of overlaps is derived as a natural\nconsequence of a branching diffusion process.\n It is shown by explicit construction that ultrametricity of the 3-replicas\noverlap distribution together with the Ghirlanda-Guerra relations determines\nthe distribution of overlaps among s replicas, for any s, in terms of the\none-overlap distribution.", "category": "cond-mat_dis-nn" }, { "text": "Optimization by thermal cycling: Thermal cycling is an heuristic optimization algorithm which consists of\ncyclically heating and quenching by Metropolis and local search procedures,\nrespectively, where the amplitude slowly decreases. In recent years, it has\nbeen successfully applied to two combinatorial optimization tasks, the\ntraveling salesman problem and the search for low-energy states of the Coulomb\nglass. In these cases, the algorithm is far more efficient than usual simulated\nannealing. In its original form the algorithm was designed only for the case of\ndiscrete variables. Its basic ideas are applicable also to a problem with\ncontinuous variables, the search for low-energy states of Lennard-Jones\nclusters.", "category": "cond-mat_dis-nn" }, { "text": "Ordering Behavior of the Two-Dimensional Ising Spin Glass with\n Long-Range Correlated Disorder: The standard two-dimensional Ising spin glass does not exhibit an ordered\nphase at finite temperature. Here, we investigate whether long-range correlated\nbonds change this behavior. The bonds are drawn from a Gaussian distribution\nwith a two-point correlation for bonds at distance r that decays as\n$(1+r^2)^{-a/2}$, $a>0$. We study numerically with exact algorithms the ground\nstate and domain wall excitations. Our results indicate that the inclusion of\nbond correlations does not lead to a spin-glass order at any finite\ntemperature. A further analysis reveals that bond correlations have a strong\neffect at local length scales, inducing ferro/antiferromagnetic domains into\nthe system. The length scale of ferro/antiferromagnetic order diverges\nexponentially as the correlation exponent approaches a critical value, $a \\to\na_c = 0$. Thus, our results suggest that the system becomes a\nferro/antiferromagnet only in the limit $a \\to 0$.", "category": "cond-mat_dis-nn" }, { "text": "Coupling and Level Repulsion in the Localized Regime: From Isolated to\n Quasi-Extended Modes: We study the interaction of Anderson localized states in an open 1D random\nsystem by varying the internal structure of the sample. As the frequencies of\ntwo states come close, they are transformed into multiply-peaked quasi-extended\nmodes. Level repulsion is observed experimentally and explained within a model\nof coupled resonators. The spectral and spatial evolution of the coupled modes\nis described in terms of the coupling coefficient and Q-factors of resonators.", "category": "cond-mat_dis-nn" }, { "text": "Absence of the non-percolating phase for percolation on the non-planar\n Hanoi network: We investigate bond percolation on the non-planar Hanoi network (HN-NP),\nwhich was studied in [Boettcher et al. Phys. Rev. E 80 (2009) 041115]. We\ncalculate the fractal exponent of a subgraph of the HN-NP, which gives a lower\nbound for the fractal exponent of the original graph. This lower bound leads to\nthe conclusion that the original system does not have a non-percolating phase,\nwhere only finite size clusters exist, for p>0, or equivalently, that the\nsystem exhibits either the critical phase, where infinitely many infinite\nclusters exist, or the percolating phase, where a unique giant component\nexists. Monte Carlo simulations support our conjecture.", "category": "cond-mat_dis-nn" }, { "text": "Neural evolution structure generation: High Entropy Alloys: We propose a method of neural evolution structures (NESs) combining\nartificial neural networks (ANNs) and evolutionary algorithms (EAs) to generate\nHigh Entropy Alloys (HEAs) structures. Our inverse design approach is based on\npair distribution functions and atomic properties and allows one to train a\nmodel on smaller unit cells and then generate a larger cell. With a speed-up\nfactor of approximately 1000 with respect to the SQSs, the NESs dramatically\nreduces computational costs and time, making possible the generation of very\nlarge structures (over 40,000 atoms) in few hours. Additionally, unlike the\nSQSs, the same model can be used to generate multiple structures with the same\nfractional composition.", "category": "cond-mat_dis-nn" }, { "text": "Anomalous Hall effect from a non-Hermitian viewpoint: Non-Hermitian descriptions often model open or driven systems away from the\nequilibrium. Nonetheless, in equilibrium electronic systems, a non-Hermitian\nnature of an effective Hamiltonian manifests itself as unconventional\nobservables such as a bulk Fermi arc and skin effects. We theoretically reveal\nthat spin-dependent quasiparticle lifetimes, which signify the non-Hermiticity\nof an effective model in the equilibrium, induce the anomalous Hall effect,\nnamely the Hall effect without an external magnetic field. We first examine the\neffect of nonmagnetic and magnetic impurities and obtain a non-Hermitian\neffective model. Then, we calculate the Kubo formula from the microscopic model\nto ascertain a non-Hermitian interpretation of the longitudinal and Hall\nconductivities. Our results elucidate the vital role of the non-Hermitian\nequilibrium nature in the quantum transport phenomena.", "category": "cond-mat_dis-nn" }, { "text": "Asymptotic Level Density of the Elastic Net Self-Organizing Feature Map: Whileas the Kohonen Self Organizing Map shows an asymptotic level density\nfollowing a power law with a magnification exponent 2/3, it would be desired to\nhave an exponent 1 in order to provide optimal mapping in the sense of\ninformation theory. In this paper, we study analytically and numerically the\nmagnification behaviour of the Elastic Net algorithm as a model for\nself-organizing feature maps. In contrast to the Kohonen map the Elastic Net\nshows no power law, but for onedimensional maps nevertheless the density\nfollows an universal magnification law, i.e. depends on the local stimulus\ndensity only and is independent on position and decouples from the stimulus\ndensity at other positions.", "category": "cond-mat_dis-nn" }, { "text": "Dynamic relaxation of a liquid cavity under amorphous boundary\n conditions: The growth of cooperatively rearranging regions was invoked long ago by Adam\nand Gibbs to explain the slowing down of glass-forming liquids. The lack of\nknowledge about the nature of the growing order, though, complicates the\ndefinition of an appropriate correlation function. One option is the\npoint-to-set correlation function, which measures the spatial span of the\ninfluence of amorphous boundary conditions on a confined system. By using a\nswap Monte Carlo algorithm we measure the equilibration time of a liquid\ndroplet bounded by amorphous boundary conditions in a model glass-former at low\ntemperature, and we show that the cavity relaxation time increases with the\nsize of the droplet, saturating to the bulk value when the droplet outgrows the\npoint-to-set correlation length. This fact supports the idea that the\npoint-to-set correlation length is the natural size of the cooperatively\nrearranging regions. On the other hand, the cavity relaxation time computed by\na standard, nonswap dynamics, has the opposite behavior, showing a very steep\nincrease when the cavity size is decreased. We try to reconcile this difference\nby discussing the possible hybridization between MCT and activated processes,\nand by introducing a new kind of amorphous boundary conditions, inspired by the\nconcept of frozen external state as an alternative to the commonly used frozen\nexternal configuration.", "category": "cond-mat_dis-nn" }, { "text": "Phase diagram for the O(n) model with defects of \"random local field\"\n type and verity of the Imry-Ma theorem: It is shown that the Imry-Ma theorem stating that in space dimensions d<4 the\nintroduction of an arbitrarily small concentration of defects of the \"random\nlocal field\" type in a system with continuous symmetry of the n-component\nvector order parameter (O(n)model) leads to the long-range order collapse and\nto the occurrence of a disordered state, is not true if the anisotropic\ndistribution of the defect-induced random local field directions in the\nn-dimensional space of the order parameter leads to the defect-induced\neffective anisotropy of the \"easy axis\" type. For a weakly anisotropic field\ndistribution, in space dimensions 20$ we find that the effective\nbarriers grow with lenghtscale as the energy differences between neighboring\nmetastable states, and demonstrate the resulting activated creep law $v\\sim\n\\exp (-C f^{-\\mu}/T)$ where the exponent $\\mu$ is obtained in a $\\epsilon=4-D$\nexpansion ($D$ is the internal dimension of the interface). Our approach also\nprovides quantitatively a new scenario for creep motion as it allows to\nidentify several intermediate lengthscales. In particular, we unveil a novel\n``depinning-like'' regime at scales larger than the activation scale, with\navalanches spreading from the thermal nucleus scale up to the much larger\ncorrelation length $R_{V}$. We predict that $R_{V}\\sim T^{-\\sigma}f^{-\\lambda\n}$ diverges at small $f$ and $T$ with exponents $\\sigma ,\\lambda$ that we\ndetermine.", "category": "cond-mat_dis-nn" }, { "text": "Energy gaps in etched graphene nanoribbons: Transport measurements on an etched graphene nanoribbon are presented. It is\nshown that two distinct voltage scales can be experimentally extracted that\ncharacterize the parameter region of suppressed conductance at low charge\ndensity in the ribbon. One of them is related to the charging energy of\nlocalized states, the other to the strength of the disorder potential. The\nlever arms of gates vary by up to 30% for different localized states which must\ntherefore be spread in position along the ribbon. A single-electron transistor\nis used to prove the addition of individual electrons to the localized states.\nIn our sample the characteristic charging energy is of the order of 10 meV, the\ncharacteristic strength of the disorder potential of the order of 100 meV.", "category": "cond-mat_dis-nn" }, { "text": "Delocalization of boundary states in disordered topological insulators: We use the method of bulk-boundary correspondence of topological invariants\nto show that disordered topological insulators have at least one delocalized\nstate at their boundary at zero energy. Those insulators which do not have\nchiral (sublattice) symmetry have in addition the whole band of delocalized\nstates at their boundary, with the zero energy state lying in the middle of the\nband. This result was previously conjectured based on the anticipated\nproperties of the supersymmetric (or replicated) sigma models with WZW-type\nterms, as well as verified in some cases using numerical simulations and a\nvariety of other arguments. Here we derive this result generally, in arbitrary\nnumber of dimensions, and without relying on the description in the language of\nsigma models.", "category": "cond-mat_dis-nn" }, { "text": "Critical eigenstates and their properties in one and two dimensional\n quasicrystals: We present exact solutions for some eigenstates of hopping models on one and\ntwo dimensional quasiperiodic tilings and show that they are \"critical\" states,\nby explicitly computing their multifractal spectra. These eigenstates are shown\nto be generically present in 1D quasiperiodic chains, of which the Fibonacci\nchain is a special case. We then describe properties of the ground states for a\nclass of tight-binding Hamiltonians on the 2D Penrose and Ammann-Beenker\ntilings. Exact and numerical solutions are seen to be in good agreement.", "category": "cond-mat_dis-nn" }, { "text": "Field-induced structural aging in glasses at ultra low temperatures: In non-equilibrium experiments on the glasses Mylar and BK7, we measured the\nexcess dielectric response after the temporary application of a strong electric\nbias field at mK--temperatures. A model recently developed describes the\nobserved long time decays qualitatively for Mylar [PRL 90, 105501, S. Ludwig,\nP. Nalbach, D. Rosenberg, D. Osheroff], but fails for BK7. In contrast, our\nresults on both samples can be described by including an additional mechanism\nto the mentioned model with temperature independent decay times of the excess\ndielectric response. As the origin of this novel process beyond the \"tunneling\nmodel\" we suggest bias field induced structural rearrangements of \"tunneling\nstates\" that decay by quantum mechanical tunneling.", "category": "cond-mat_dis-nn" }, { "text": "Ising Model Scaling Behaviour on z-Preserving Small-World Networks: We have investigated the anomalous scaling behaviour of the Ising model on\nsmall-world networks based on 2- and 3-dimensional lattices using Monte Carlo\nsimulations. Our main result is that even at low $p$, the shift in the critical\ntemperature $\\Delta T_c$ scales as $p^{s}$, with $s \\approx 0.50$ for 2-D\nsystems, $s \\approx 0.698$ for 3-D and $s \\approx 0.75$ for 4-D. We have also\nverified that a $z$-preserving rewiring algorithm still exhibits small-world\neffects and yet is more directly comparable with the conventional Ising model;\nthe small-world effect is due to enhanced long-range correlations and not the\nchange in effective dimension. We find the critical exponents $\\beta$ and $\\nu$\nexhibit a monotonic change between an Ising-like transition and mean-field\nbehaviour in 2- and 3-dimensional systems.", "category": "cond-mat_dis-nn" }, { "text": "Fragmentation of a circular disc by projectiles: The fragmentation of a two-dimensional circular disc by lateral impact is\ninvestigated using a cell model of brittle solid. The disc is composed of\nnumerous unbreakable randomly shaped convex polygons connected together by\nsimple elastic beams that break when bent or stretched beyond a certain limit.\nWe found that the fragment mass distribution follows a power law with an\nexponent close to 2 independent of the system size. We also observed two types\nof crack patterns: radial cracks starting from the impact point and cracks\nperpendicular to the radial ones. Simulations revealed that there exists a\ncritical projectile energy, above which the target breaks into numerous smaller\npieces, and below which it suffers only damage in the form of cracks. Our\ntheoretical results are in a reasonable agreement with recent experimental\nfindings on the fragmentation of discs.", "category": "cond-mat_dis-nn" }, { "text": "Direct Measurement of Random Fields in the $LiHo_xY_{1-x}F_4$ Crystal: The random field Ising model (RFIM) is central to the study of disordered\nsystems. Yet, for a long time it eluded realization in ferromagnetic systems\nbecause of the difficulty to produce locally random magnetic fields. Recently\nit was shown that in anisotropic dipolar magnetic insulators, the archetypal of\nwhich is the $LiHo_xY_{1-x}F_4$ system, the RFIM can be realized in both\nferromagnetic and spin glass phases. The interplay between an applied\ntransverse field and the offdiagonal terms of the dipolar interaction produce\neffective longitudinal fields, which are random in sign and magnitude as a\nresult of spatial dilution. In this paper we use exact numerical\ndiagonalization of the full Hamiltonian of Ho pairs in $LiHo_xY_{1-x}F_4$ to\ncalculate the effective longitudinal field beyond the perturbative regime. In\nparticular, we find that nearby spins can experience an effective field larger\nthan the intrinsic dipolar broadening (of quantum states in zero field) which\ncan therefore be evidenced in experiments. We then calculate the magnetization\nand susceptibility under several experimental protocols, and show how these\nprotocols can produce direct measurement of the effective longitudinal field.", "category": "cond-mat_dis-nn" }, { "text": "The Ising Spin Glass in dimension five: link overlaps: Extensive simulations are made of the link overlap in five dimensional Ising\nSpin Glasses (ISGs) through and below the ordering transition. Moments of the\nmean link overlap distributions (the kurtosis and the skewness) show clear\ncritical maxima at the ISG ordering temperature. These criteria can be used as\nefficient tools to identify a freezing transition quite generally and in any\ndimension. In the ISG ordered phase the mean link overlap distribution develops\na strong two peak structure, with the link overlap spectra of individual\nsamples becoming very heterogeneous. There is no tendency towards a \"trivial\"\nuniversal single peak distribution in the range of size and temperature covered\nby the data.", "category": "cond-mat_dis-nn" }, { "text": "Quantum exploration of high-dimensional canyon landscapes: Canyon landscapes in high dimension can be described as manifolds of small,\nbut extensive dimension, immersed in a higher dimensional ambient space and\ncharacterized by a zero potential energy on the manifold. Here we consider the\nproblem of a quantum particle exploring a prototype of a high-dimensional\nrandom canyon landscape. We characterize the thermal partition function and\nshow that around the point where the classical phase space has a satisfiability\ntransition so that zero potential energy canyons disappear, moderate quantum\nfluctuations have a deleterious effect and induce glassy phases at temperature\nwhere classical thermal fluctuations alone would thermalize the system.\nSurprisingly we show that even when, classically, diffusion is expected to be\nunbounded in space, the interplay between quantum fluctuations and the\nrandomness of the canyon landscape conspire to have a confining effect.", "category": "cond-mat_dis-nn" }, { "text": "Patterns of link reciprocity in directed networks: We address the problem of link reciprocity, the non-random presence of two\nmutual links between pairs of vertices. We propose a new measure of reciprocity\nthat allows the ordering of networks according to their actual degree of\ncorrelation between mutual links. We find that real networks are always either\ncorrelated or anticorrelated, and that networks of the same type (economic,\nsocial, cellular, financial, ecological, etc.) display similar values of the\nreciprocity. The observed patterns are not reproduced by current models. This\nleads us to introduce a more general framework where mutual links occur with a\nconditional connection probability. In some of the studied networks we discuss\nthe form of the conditional connection probability and the size dependence of\nthe reciprocity.", "category": "cond-mat_dis-nn" }, { "text": "Finite-Temperature Fluid-Insulator Transition of Strongly Interacting 1D\n Disordered Bosons: We consider the many-body localization-delocalization transition for strongly\ninteracting one- dimensional disordered bosons and construct the full picture\nof finite temperature behavior of this system. This picture shows two\ninsulator-fluid transitions at any finite temperature when varying the\ninteraction strength. At weak interactions an increase in the interaction\nstrength leads to insulator->fluid transition, and for large interactions one\nhas a reentrance to the insulator regime.", "category": "cond-mat_dis-nn" }, { "text": "Excess wing in glass-forming glycerol and LiCl-glycerol mixtures\n detected by neutron scattering: The relaxational dynamics in glass-forming glycerol and glycerol mixed with\nLiCl is in-vestigated using different neutron scattering techniques. The\nperformed neutron spin-echo experiments, which extend up to relatively long\nrelaxation-time scales of the order of 10 ns, should allow for the detection of\ncontributions from the so-called excess wing. This phenomenon, whose\nmicroscopic origin is controversially discussed, arises in a variety of glass\nformers and, until now, was almost exclusively investigated by dielectric\nspectros-copy and light scattering. Here we show that the relaxational process\ncausing the excess wing also can be detected by neutron scattering, which\ndirectly couples to density fluctua-tions.", "category": "cond-mat_dis-nn" }, { "text": "Temperature-dependent criticality in random 2D Ising models: We consider 2D random Ising ferromagnetic models, where quenched disorder is\nrepresented either by random local magnetic fields (Random Field Ising Model)\nor by a random distribution of interaction couplings (Random Bond Ising Model).\nIn both cases we first perform zero- and finite-temperature Monte-Carlo\nsimulations to determine how the critical temperature depends on the disorder\nparameter. We then focus on the reversal transition triggered by an external\nfield, and study the associated Barkhausen noise. Our main result is that the\ncritical exponents characterizing the power-law associated with the Barkhausen\nnoise exhibit a temperature dependence in line with existing experimental\nobservations.", "category": "cond-mat_dis-nn" }, { "text": "Dynamics of weakly coupled random antiferromagnetic quantum spin chains: We study the low-energy collective excitations and dynamical response\nfunctions of weakly coupled random antiferromagnetic spin-1/2 chains. The\ninterchain coupling leads to Neel order at low temperatures. We use the\nreal-space renormalization group technique to tackle the intrachain couplings\nand treat the interchain couplings within the Random Phase Approximation (RPA).\nWe show that the system supports collective spin wave excitations, and\ncalculate the spin wave velocity and spectra weight within RPA. Comparisons\nwill be made with inelastic neutron scattering experiments\nquasi-one-dimensional disordered spin systems such as doped CuGeO$_3$", "category": "cond-mat_dis-nn" }, { "text": "The Exponential Capacity of Dense Associative Memories: Recent generalizations of the Hopfield model of associative memories are able\nto store a number $P$ of random patterns that grows exponentially with the\nnumber $N$ of neurons, $P=\\exp(\\alpha N)$. Besides the huge storage capacity,\nanother interesting feature of these networks is their connection to the\nattention mechanism which is part of the Transformer architectures widely\napplied in deep learning. In this work, we study a generic family of pattern\nensembles using a statistical mechanics analysis which gives exact asymptotic\nthresholds for the retrieval of a typical pattern, $\\alpha_1$, and lower bounds\nfor the maximum of the load $\\alpha$ for which all patterns can be retrieved,\n$\\alpha_c$, as well as sizes of attraction basins. We discuss in detail the\ncases of Gaussian and spherical patterns, and show that they display rich and\nqualitatively different phase diagrams.", "category": "cond-mat_dis-nn" }, { "text": "Renormalization of Oscillator Lattices with Disorder: A real-space renormalization transformation is constructed for lattices of\nnon-identical oscillators with dynamics of the general form\n$d\\phi_{k}/dt=\\omega_{k}+g\\sum_{l}f_{lk}(\\phi_{l},\\phi_{k})$. The\ntransformation acts on ensembles of such lattices. Critical properties\ncorresponding to a second order phase transition towards macroscopic\nsynchronization are deduced. The analysis is potentially exact, but relies in\npart on unproven assumptions. Numerically, second order phase transitions with\nthe predicted properties are observed as $g$ increases in two structurally\ndifferent, two-dimensional oscillator models. One model has smooth coupling\n$f_{lk}(\\phi_{l},\\phi_{k})=\\phi(\\phi_{l}-\\phi_{k})$, where $\\phi(x)$ is\nnon-odd. The other model is pulse-coupled, with\n$f_{lk}(\\phi_{l},\\phi_{k})=\\delta(\\phi_{l})\\phi(\\phi_{k})$. Lower bounds for\nthe critical dimensions for different types of coupling are obtained. For\nnon-odd coupling, macroscopic synchronization cannot be ruled out for any\ndimension $D\\geq 1$, whereas in the case of odd coupling, the well-known result\nthat it can be ruled out for $D< 3$ is regained.", "category": "cond-mat_dis-nn" }, { "text": "Numerical verification of universality for the Anderson transition: We analyze the scaling behavior of the higher Lyapunov exponents at the\nAnderson transition. We estimate the critical exponent and verify its\nuniversality and that of the critical conductance distribution for box,\nGaussian and Lorentzian distributions of the random potential.", "category": "cond-mat_dis-nn" }, { "text": "Spectral description of the dynamics of ultracold interacting bosons in\n disordered lattices: We study the dynamics of a nonlinear one-dimensional disordered system from a\nspectral point of view. The spectral entropy and the Lyapunov exponent are\nextracted from the short time dynamics, and shown to give a pertinent\ncharacterization of the different dynamical regimes. The chaotic and\nself-trapped regimes are governed by log-normal laws whose origin is traced to\nthe exponential shape of the eigenstates of the linear problem. These\nquantities satisfy scaling laws depending on the initial state and explain the\nsystem behaviour at longer times.", "category": "cond-mat_dis-nn" }, { "text": "Creep motion of an elastic string in a random potential: We study the creep motion of an elastic string in a two dimensional pinning\nlandscape by Langevin dynamics simulations. We find that the Velocity-Force\ncharacteristics are well described by the creep formula predicted from\nphenomenological scaling arguments. We analyze the creep exponent $\\mu$, and\nthe roughness exponent $\\zeta$. Two regimes are identified: when the\ntemperature is larger than the strength of the disorder we find $\\mu \\approx\n1/4$ and $\\zeta \\approx 2/3$, in agreement with the\nquasi-equilibrium-nucleation picture of creep motion; on the contrary, lowering\nenough the temperature, the values of $\\mu$ and $\\zeta$ increase showing a\nstrong violation of the latter picture.", "category": "cond-mat_dis-nn" }, { "text": "Analysis of Many-body Localization Landscapes and Fock Space Morphology\n via Persistent Homology: We analyze functionals that characterize the distribution of eigenstates in\nFock space through a tool derived from algebraic topology: persistent homology.\nDrawing on recent generalizations of the localization landscape applicable to\nmid-spectrum eigenstates, we introduce several novel persistent homology\nobservables in the context of many-body localization that exhibit transitional\nbehavior near the critical point. We demonstrate that the persistent homology\napproach to localization landscapes and, in general, functionals on the Fock\nspace lattice offer insights into the structure of eigenstates unobtainable by\ntraditional means.", "category": "cond-mat_dis-nn" }, { "text": "Structure and Relaxation Dynamics of a Colloidal Gel: Using molecular dynamics computer simulations we investigate the structural\nand dynamical properties of a simple model for a colloidal gel at low volume\nfraction. We find that at low T the system is forming an open percolating\ncluster, without any sign of a phase separation. The nature of the relaxation\ndynamics depends strongly on the length scale/wave-vector considered and can be\ndirectly related to the geometrical properties of the spanning cluster.", "category": "cond-mat_dis-nn" }, { "text": "Probing tails of energy distributions using importance-sampling in the\n disorder with a guiding function: We propose a simple and general procedure based on a recently introduced\napproach that uses an importance-sampling Monte Carlo algorithm in the disorder\nto probe to high precision the tails of ground-state energy distributions of\ndisordered systems. Our approach requires an estimate of the ground-state\nenergy distribution as a guiding function which can be obtained from\nsimple-sampling simulations. In order to illustrate the algorithm, we compute\nthe ground-state energy distribution of the Sherrington-Kirkpatrick mean-field\nIsing spin glass to eighteen orders of magnitude. We find that the ground-state\nenergy distribution in the thermodynamic limit is well fitted by a modified\nGumbel distribution as previously predicted, but with a value of the slope\nparameter m which is clearly larger than 6 and of the order 11.", "category": "cond-mat_dis-nn" }, { "text": "Statistical Properties of the one dimensional Anderson model relevant\n for the Nonlinear Schr\u00f6dinger Equation in a random potential: The statistical properties of overlap sums of groups of four eigenfunctions\nof the Anderson model for localization as well as combinations of four\neigenenergies are computed. Some of the distributions are found to be scaling\nfunctions, as expected from the scaling theory for localization. These enable\nto compute the distributions in regimes that are otherwise beyond the\ncomputational resources. These distributions are of great importance for the\nexploration of the Nonlinear Schr\\\"odinger Equation (NLSE) in a random\npotential since in some explorations the terms we study are considered as noise\nand the present work describes its statistical properties.", "category": "cond-mat_dis-nn" }, { "text": "Tower of quantum scars in a partially many-body localized system: Isolated quantum many-body systems are often well-described by the eigenstate\nthermalization hypothesis. There are, however, mechanisms that cause different\nbehavior: many-body localization and quantum many-body scars. Here, we show how\none can find disordered Hamiltonians hosting a tower of scars by adapting a\nknown method for finding parent Hamiltonians. Using this method, we construct a\nspin-1/2 model which is both partially localized and contains scars. We\ndemonstrate that the model is partially localized by studying numerically the\nlevel spacing statistics and bipartite entanglement entropy. As disorder is\nintroduced, the adjacent gap ratio transitions from the Gaussian orthogonal\nensemble to the Poisson distribution and the entropy shifts from volume-law to\narea-law scaling. We investigate the properties of scars in a partially\nlocalized background and compare with a thermal background. At strong disorder,\nstates initialized inside or outside the scar subspace display different\ndynamical behavior but have similar entanglement entropy and Schmidt gap. We\ndemonstrate that localization stabilizes scar revivals of initial states with\nsupport both inside and outside the scar subspace. Finally, we show how strong\ndisorder introduces additional approximate towers of eigenstates.", "category": "cond-mat_dis-nn" }, { "text": "Delocalization of topological surface states by diagonal disorder in\n nodal loop semimetals: The effect of Anderson diagonal disorder on the topological surface\n(``drumhead'') states of a Weyl nodal loop semimetal is addressed. Since\ndiagonal disorder breaks chiral symmetry, a winding number cannot be defined.\nSeen as a perturbation, the weak random potential mixes the clean exponentially\nlocalized drumhead states of the semimetal, thereby producing two effects: (i)\nthe algebraic decay of the surface states into the bulk; (ii) a broadening of\nthe low energy density of surface states of the open system due to degeneracy\nlifting. This behavior persists with increasing disorder, up to the bulk\nsemimetal-to-metal transition at the critical disorder $W_{c}$. Above $W_{c}$,\nthe surface states hybridize with bulk states and become extended into the\nbulk.", "category": "cond-mat_dis-nn" }, { "text": "Probing the dynamics of Anderson localization through spatial mapping: We study (1+1)D transverse localization of electromagnetic radiation at\nmicrowave frequencies directly by two-dimensional spatial scans. Since the\nlongitudinal direction can be mapped onto time, our experiments provide unique\nsnapshots of the build-up of localized waves. The evolution of the wave\nfunctions is compared with numerical calculations. Dissipation is shown to have\nno effect on the occurrence of transverse localization. Oscillations of the\nwave functions are observed in space and explained in terms of a beating\nbetween the eigenstates.", "category": "cond-mat_dis-nn" }, { "text": "Supermetallic and Trapped States in Periodically Kicked Lattices: A periodically driven lattice with two commensurate spatial periodicities is\nfound to exhibit super metallic states characterized by enhancements in wave\npacket spreading and entropy. These resonances occur at critical values of\nparameters where multi-band dispersion curves reduce to a universal function\nthat is topologically a circle and the effective quantum dynamics describes\nfree propagation. Sandwiching every resonant state are a pair of anti-resonant\n{\\it trapped states} distinguished by dips in entropy where the transport, as\nseen in the spreading rate, is only somewhat inhibited. Existing in gapless\nphases fo the spectrum, a sequence of these peaks and dips are interspersed by\ngapped phases assocated with flat band states where both the wave packet\nspreading as well as the entropy exhibit local minima.", "category": "cond-mat_dis-nn" }, { "text": "Multifractality of ab initio wave functions in doped semiconductors: In Refs. [1,2] we have shown how a combination of modern linear-scaling DFT,\ntogether with a subsequent use of large, effective tight-binding Hamiltonians,\nallows to compute multifractal wave functions yielding the critical properties\nof the Anderson metal-insulator transition (MIT) in doped semiconductors. This\ncombination allowed us to construct large and atomistically realistic samples\nof sulfur-doped silicon (Si:S). The critical properties of such systems and the\nexistence of the MIT are well known, but experimentally determined values of\nthe critical exponent $\\nu$ close to the transition have remained different\nfrom those obtained by the standard tight-binding Anderson model. In Ref. [1],\nwe found that this ``exponent puzzle'' can be resolved when using our novel\n\\emph{ab initio} approach based on scaling of multifractal exponents in the\nrealistic impurity band for Si:S. Here, after a short review of\nmultifractality, we give details of the multifractal analysis as used in [1]\nand show the obtained \\emph{critical} multifractal spectrum at the MIT for\nSi:S.", "category": "cond-mat_dis-nn" }, { "text": "Coexistence of localization and transport in many-body two-dimensional\n Aubry-Andr\u00e9 models: Whether disordered and quasiperiodic many-body quantum systems host a\nlong-lived localized phase in the thermodynamic limit has been the subject of\nintense recent debate. While in one dimension substantial evidence for the\nexistence of such a many-body localized (MBL) phase exists, the behavior in\nhigher dimensions remains an open puzzle. In two-dimensional disordered\nsystems, for instance, it has been argued that rare regions may lead to\nthermalization of the whole system through a mechanism dubbed the avalanche\ninstability. In quasiperiodic systems, rare regions are altogether absent and\nthe fate of a putative many-body localized phase has hitherto remained largely\nunexplored. In this work, we investigate the localization properties of two\nmany-body quasiperiodic models, which are two-dimensional generalizations of\nthe Aubry-Andr\\'e model. By studying the out-of-equilibrium dynamics of large\nsystems, we find a long-lived MBL phase, in contrast to random systems.\nFurthermore, we show that deterministic lines of weak potential, which appear\nin investigated quasiperiodic models, support large-scale transport, while the\nsystem as a whole does not thermalize. Our results demonstrate that\nquasiperiodic many-body systems have the remarkable and counter-intuitive\ncapability of exhibiting coexisting localization and transport properties - a\nphenomenon reminiscent of the behavior of supersolids. Our findings are of\ndirect experimental relevance and can be tested, for instance, using\nstate-of-the-art cold atomic systems.", "category": "cond-mat_dis-nn" }, { "text": "Failure Probabilities and Tough-Brittle Crossover of Heterogeneous\n Materials with Continuous Disorder: The failure probabilities or the strength distributions of heterogeneous 1D\nsystems with continuous local strength distribution and local load sharing have\nbeen studied using a simple, exact, recursive method. The fracture behavior\ndepends on the local bond-strength distribution, the system size, and the\napplied stress, and crossovers occur as system size or stress changes. In the\nbrittle region, systems with continuous disorders have a failure probability of\nthe modified-Gumbel form, similar to that for systems with percolation\ndisorder. The modified-Gumbel form is of special significance in weak-stress\nsituations. This new recursive method has also been generalized to calculate\nexactly the failure probabilities under various boundary conditions, thereby\nillustrating the important effect of surfaces in the fracture process.", "category": "cond-mat_dis-nn" }, { "text": "Crossovers in ScaleFree Networks on Geographical Space: Complex networks are characterized by several topological properties: degree\ndistribution, clustering coefficient, average shortest path length, etc. Using\na simple model to generate scale-free networks embedded on geographical space,\nwe analyze the relationship between topological properties of the network and\nattributes (fitness and location) of the vertices in the network. We find there\nare two crossovers for varying the scaling exponent of the fitness\ndistribution.", "category": "cond-mat_dis-nn" }, { "text": "\"Single Ring Theorem\" and the Disk-Annulus Phase Transition: Recently, an analytic method was developed to study in the large $N$ limit\nnon-hermitean random matrices that are drawn from a large class of circularly\nsymmetric non-Gaussian probability distributions, thus extending the existing\nGaussian non-hermitean literature. One obtains an explicit algebraic equation\nfor the integrated density of eigenvalues from which the Green's function and\naveraged density of eigenvalues could be calculated in a simple manner. Thus,\nthat formalism may be thought of as the non-hermitean analog of the method due\nto Br\\'ezin, Itzykson, Parisi and Zuber for analyzing hermitean non-Gaussian\nrandom matrices. A somewhat surprising result is the so called \"Single Ring\"\ntheorem, namely, that the domain of the eigenvalue distribution in the complex\nplane is either a disk or an annulus. In this paper we extend previous results\nand provide simple new explicit expressions for the radii of the eigenvalue\ndistiobution and for the value of the eigenvalue density at the edges of the\neigenvalue distribution of the non-hermitean matrix in terms of moments of the\neigenvalue distribution of the associated hermitean matrix. We then present\nseveral numerical verifications of the previously obtained analytic results for\nthe quartic ensemble and its phase transition from a disk shaped eigenvalue\ndistribution to an annular distribution. Finally, we demonstrate numerically\nthe \"Single Ring\" theorem for the sextic potential, namely, the potential of\nlowest degree for which the \"Single Ring\" theorem has non-trivial consequences.", "category": "cond-mat_dis-nn" }, { "text": "Exact non-Hermitian mobility edges and robust flat bands in\n two-dimensional Lieb lattices with imaginary quasiperiodic potentials: The mobility edge (ME) is a critical energy delineates the boundary between\nextended and localized states within the energy spectrum, and it plays a\ncrucial role in understanding the metal-insulator transition in disordered or\nquasiperiodic systems. While there have been extensive studies on MEs in\none-dimensional non-Hermitian (NH) quasiperiodic lattices recently, the\ninvestigation of exact NH MEs in two-dimensional (2D) cases remains rare. In\nthe present study, we introduce a 2D dissipative Lieb lattice (DLL) model with\nimaginary quasiperiodic potentials applied solely to the vertices of the Lieb\nlattice. By mapping this DLL model to the 2D NH Aubry-Andr{\\'e}-Harper (AAH)\nmodel, we analytically derive the exact ME and find it associated with the\nabsolute eigenenergies. We find that the eigenvalues of extended states are\npurely imaginary when the quasiperiodic potential is strong enough.\nAdditionally, we demonstrate that the introduction of imaginary quasiperiodic\npotentials does not disrupt the flat bands inherent in the system. Finally, we\npropose a theoretical framework for realizing our model using the Lindblad\nmaster equation. Our results pave the way for further investigation of exact NH\nMEs and flat bands in 2D dissipative quasiperiodic systems.", "category": "cond-mat_dis-nn" }, { "text": "Adaptive cluster expansion for the inverse Ising problem: convergence,\n algorithm and tests: We present a procedure to solve the inverse Ising problem, that is to find\nthe interactions between a set of binary variables from the measure of their\nequilibrium correlations. The method consists in constructing and selecting\nspecific clusters of variables, based on their contributions to the\ncross-entropy of the Ising model. Small contributions are discarded to avoid\noverfitting and to make the computation tractable. The properties of the\ncluster expansion and its performances on synthetic data are studied. To make\nthe implementation easier we give the pseudo-code of the algorithm.", "category": "cond-mat_dis-nn" }, { "text": "Topology invariance in Percolation Thresholds: An universal invariant for site and bond percolation thresholds (p_{cs} and\np_{cb} respectively) is proposed. The invariant writes\n{p_{cs}}^{1/a_s}{p_{cb}}^{-1/a_b}=\\delta/d where a_s, a_b and \\delta are\npositive constants,and d the space dimension. It is independent of the\ncoordination number, thus exhibiting a topology invariance at any d.The formula\nis checked against a large class of percolation problems, including percolation\nin non-Bravais lattices and in aperiodic lattices as well as rigid percolation.\nThe invariant is satisfied within a relative error of \\pm 5% for all the twenty\nlattices of our sample at d=2, d=3, plus all hypercubes up to d=6.", "category": "cond-mat_dis-nn" }, { "text": "Exact Ground State Properties of Disordered Ising-Systems: Exact ground states are calculated with an integer optimization algorithm for\ntwo and three dimensional site-diluted Ising antiferromagnets in a field (DAFF)\nand random field Ising ferromagnets (RFIM). We investigate the structure and\nthe size-distribution of the domains of the ground state and compare it to\nearlier results from Monte Carlo simulations for finite temperature. Although\nDAFF and RFIM are thought to be in the same universality class we found\nessential differences between these systems as far as the domain properties are\nconcerned. For the DAFF the ground states consist of fractal domains with a\nbroad size distribution that can be described by a power law with exponential\ncut-off. For the RFIM the limiting case of the size distribution and structure\nof the domains for strong random fields is the size distribution and structure\nof the clusters of the percolation problem with a field dependent lower\ncut-off. The domains are fractal and in three dimensions nearly all spins\nbelong to two large infinite domains of up- and down spins - the system is in a\ntwo-domain state.", "category": "cond-mat_dis-nn" }, { "text": "Towards quantization Conway Game of Life: Classical stochastic Conway Game of Life is expressed by the dissipative\nSchr\\\"odinger equation and dissipative tight-binding model. This is conducted\nat the prize of usage of time dependent anomalous non-Hermitian Hamiltonians as\nwith occurrence of complex value potential that do not preserve the\nnormalization of wave-function and thus allows for mimicking creationism or\nannihilationism of cellular automaton. Simply saying time-dependent complex\nvalue eigenenergies are similar to complex values of resonant frequencies in\nelectromagnetic resonant cavities reflecting presence of dissipation that\nreflects energy leaving the system or being pumped into the system. At the same\ntime various aspects of thermodynamics were observed in cellular automata that\ncan be later reformulated by quantum mechanical pictures. The usage of Shannon\nentropy and mass equivalence to energy points definition of cellular automata\ntemperature. Contrary to intuitive statement the system dynamical equilibrium\nis always reflected by negative temperatures. Diffusion of mass, energy and\ntemperature as well as phase of proposed wave function is reported and can be\ndirectly linked with second thermodynamics law approximately valid for the\nsystem, where neither mass nor energy is conserved. The concept of\ncomplex-valued mass mimics wave-function behavior. Equivalence an anomalous\nsecond Fick law and dissipative Schr\\\"odinger equation is given. Dissipative\nConway Game of Life tight-binding Hamiltonian is given using phenomenological\njustification.", "category": "cond-mat_dis-nn" }, { "text": "Effect of Strong Disorder on 3-Dimensional Chiral Topological\n Insulators: Phase Diagrams, Maps of the Bulk Invariant and Existence of\n Topological Extended Bulk States: The effect of strong disorder on chiral-symmetric 3-dimensional lattice\nmodels is investigated via analytical and numerical methods. The phase diagrams\nof the models are computed using the non-commutative winding number, as\nfunctions of disorder strength and model's parameters. The\nlocalized/delocalized characteristic of the quantum states is probed with level\nstatistics analysis. Our study re-confirms the accurate quantization of the\nnon-commutative winding number in the presence of strong disorder, and its\neffectiveness as a numerical tool. Extended bulk states are detected above and\nbelow the Fermi level, which are observed to undergo the so called \"levitation\nand pair annihilation\" process when the system is driven through a topological\ntransition. This suggests that the bulk invariant is carried by these extended\nstates, in stark contrast with the 1-dimensional case where the extended states\nare completely absent and the bulk invariant is carried by the localized\nstates.", "category": "cond-mat_dis-nn" }, { "text": "Interdependent networks with correlated degrees of mutually dependent\n nodes: We study a problem of failure of two interdependent networks in the case of\ncorrelated degrees of mutually dependent nodes. We assume that both networks (A\nand B) have the same number of nodes $N$ connected by the bidirectional\ndependency links establishing a one-to-one correspondence between the nodes of\nthe two networks in a such a way that the mutually dependent nodes have the\nsame number of connectivity links, i.e. their degrees coincide. This implies\nthat both networks have the same degree distribution $P(k)$. We call such\nnetworks correspondently coupled networks (CCN). We assume that the nodes in\neach network are randomly connected. We define the mutually connected clusters\nand the mutual giant component as in earlier works on randomly coupled\ninterdependent networks and assume that only the nodes which belong to the\nmutual giant component remain functional. We assume that initially a $1-p$\nfraction of nodes are randomly removed due to an attack or failure and find\nanalytically, for an arbitrary $P(k)$, the fraction of nodes $\\mu(p)$ which\nbelong to the mutual giant component. We find that the system undergoes a\npercolation transition at certain fraction $p=p_c$ which is always smaller than\nthe $p_c$ for randomly coupled networks with the same $P(k)$. We also find that\nthe system undergoes a first order transition at $p_c>0$ if $P(k)$ has a finite\nsecond moment. For the case of scale free networks with $2<\\lambda \\leq 3$, the\ntransition becomes a second order transition. Moreover, if $\\lambda<3$ we find\n$p_c=0$ as in percolation of a single network. For $\\lambda=3$ we find an exact\nanalytical expression for $p_c>0$. Finally, we find that the robustness of CCN\nincreases with the broadness of their degree distribution.", "category": "cond-mat_dis-nn" }, { "text": "Memory effects in transport through a hopping insulator: Understanding\n two-dip experiments: We discuss memory effects in the conductance of hopping insulators due to\nslow rearrangements of many-electron clusters leading to formation of polarons\nclose to the electron hopping sites. An abrupt change in the gate voltage and\ncorresponding shift of the chemical potential change populations of the hopping\nsites, which then slowly relax due to rearrangements of the clusters. As a\nresult, the density of hopping states becomes time dependent on a scale\nrelevant to rearrangement of the structural defects leading to the excess time\ndependent conductivity.", "category": "cond-mat_dis-nn" }, { "text": "Long-range correlations of density in a Bose-Einstein condensate\n expanding in a random potential: We study correlations of atomic density in a weakly interacting Bose-Einstein\ncondensate, expanding diffusively in a random potential. We show that these\ncorrelations are long-range and that they are strongly enhanced at long times.\nDensity at distant points exhibits negative correlations.", "category": "cond-mat_dis-nn" }, { "text": "Many-body localization, thermalization, and entanglement: Thermalizing quantum systems are conventionally described by statistical\nmechanics at equilibrium. However, not all systems fall into this category,\nwith many body localization providing a generic mechanism for thermalization to\nfail in strongly disordered systems. Many-body localized (MBL) systems remain\nperfect insulators at non-zero temperature, which do not thermalize and\ntherefore cannot be described using statistical mechanics. In this Colloquium\nwe review recent theoretical and experimental advances in studies of MBL\nsystems, focusing on the new perspective provided by entanglement and\nnon-equilibrium experimental probes such as quantum quenches. Theoretically,\nMBL systems exhibit a new kind of robust integrability: an extensive set of\nquasi-local integrals of motion emerges, which provides an intuitive\nexplanation of the breakdown of thermalization. A description based on\nquasi-local integrals of motion is used to predict dynamical properties of MBL\nsystems, such as the spreading of quantum entanglement, the behavior of local\nobservables, and the response to external dissipative processes. Furthermore,\nMBL systems can exhibit eigenstate transitions and quantum orders forbidden in\nthermodynamic equilibrium. We outline the current theoretical understanding of\nthe quantum-to-classical transition between many-body localized and ergodic\nphases, and anomalous transport in the vicinity of that transition.\nExperimentally, synthetic quantum systems, which are well-isolated from an\nexternal thermal reservoir, provide natural platforms for realizing the MBL\nphase. We review recent experiments with ultracold atoms, trapped ions,\nsuperconducting qubits, and quantum materials, in which different signatures of\nmany-body localization have been observed. We conclude by listing outstanding\nchallenges and promising future research directions.", "category": "cond-mat_dis-nn" }, { "text": "Anderson localization of a Bose-Einstein condensate in a 3D random\n potential: We study the effect of Anderson localization on the expansion of a\nBose-Einstein condensate, released from a harmonic trap, in a 3D random\npotential. We use scaling arguments and the self-consistent theory of\nlocalization to show that the long-time behavior of the condensate density is\ncontrolled by a single parameter equal to the ratio of the mobility edge and\nthe chemical potential of the condensate. We find that the two critical\nexponents of the localization transition determine the evolution of the\ncondensate density in time and space.", "category": "cond-mat_dis-nn" }, { "text": "Dimensional Dependence of Critical Exponent of the Anderson Transition\n in the Orthogonal Universality Class: We report improved numerical estimates of the critical exponent of the\nAnderson transition in Anderson's model of localization in $d=4$ and $d=5$\ndimensions. We also report a new Borel-Pad\\'e analysis of existing $\\epsilon$\nexpansion results that incorporates the asymptotic behaviour for $d\\to \\infty$\nand gives better agreement with available numerical results.", "category": "cond-mat_dis-nn" }, { "text": "Phase Transition in the Random Anisotropy Model: The influence of a local anisotropy of random orientation on a ferromagnetic\nphase transition is studied for two cases of anisotropy axis distribution. To\nthis end a model of a random anisotropy magnet is analyzed by means of the\nfield theoretical renormalization group approach in two loop approximation\nrefined by a resummation of the asymptotic series. The one-loop result of\nAharony indicating the absence of a second-order phase transition for an\nisotropic distribution of random anisotropy axis at space dimension $d<4$ is\ncorroborated. For a cubic distribution the accessible stable fixed point leads\nto disordered Ising-like critical exponents.", "category": "cond-mat_dis-nn" }, { "text": "Universality and universal finite-size scaling functions in\n four-dimensional Ising spin glasses: We study the four-dimensional Ising spin glass with Gaussian and bond-diluted\nbimodal distributed interactions via large-scale Monte Carlo simulations and\nshow via an extensive finite-size scaling analysis that four-dimensional Ising\nspin glasses obey universality.", "category": "cond-mat_dis-nn" }, { "text": "From power law to Anderson localization in nonlinear Schr\u00f6dinger\n equation with nonlinear randomness: We study the propagation of coherent waves in a nonlinearly-induced random\npotential, and find regimes of self-organized criticality and other regimes\nwhere the nonlinear equivalent of Anderson localization prevails. The regime of\nself-organized criticality leads to power-law decay of transport [Phys. Rev.\nLett. 121, 233901 (2018)], whereas the second regime exhibits exponential\ndecay.", "category": "cond-mat_dis-nn" }, { "text": "The Leontovich boundary conditions and calculation of effective\n impedance of inhomogeneous metal: We bring forward rather simple algorithm allowing us to calculate the\neffective impedance of inhomogeneous metals in the frequency region where the\nlocal Leontovich (the impedance) boundary conditions are justified. The\ninhomogeneity is due to the properties of the metal or/and the surface\nroughness. Our results are nonperturbative ones with respect to the\ninhomogeneity amplitude. They are based on the recently obtained exact result\nfor the effective impedance of inhomogeneous metals with flat surfaces.\nOne-dimension surfaces inhomogeneities are examined. Particular attention is\npaid to the influence of generated evanescent waves on the reflection\ncharacteristics. We show that if the surface roughness is rather strong, the\nelement of the effective impedance tensor relating to the p- polarization state\nis much greater than the input local impedance. As examples, we calculate: i)\nthe effective impedance for a flat surface with strongly nonhomogeneous\nperiodic strip-like local impedance; ii) the effective impedance associated\nwith one-dimensional lamellar grating. For the problem (i) we also present\nequations for the forth lines of the Pointing vector in the vicinity of the\nsurface.", "category": "cond-mat_dis-nn" }, { "text": "Comment on \"Erratum: Collective modes and gapped momentum states in\n liquid Ga:Experiment, theory, and simulation\": We show, that the theoretical expression for the dispersion of collective\nexcitations reported in [Phys. Rev. B {\\bf 103}, 099901 (2021)], at variance\nwith what was claimed in the paper, does not account for the energy\nfluctuations and does not tend in the long-wavelegth limit to the correct\nhydrodynamic dispersion law.", "category": "cond-mat_dis-nn" }, { "text": "Quantum transport of atomic matterwaves in anisotropic 2D and 3D\n disorder: The macroscopic transport properties in a disordered potential, namely\ndiffusion and weak/strong localization, closely depend on the microscopic and\nstatistical properties of the disorder itself. This dependence is rich of\ncounter-intuitive consequences. It can be particularly exploited in matter wave\nexperiments, where the disordered potential can be tailored and controlled, and\nanisotropies are naturally present. In this work, we apply a perturbative\nmicroscopic transport theory and the self-consistent theory of Anderson\nlocalization to study the transport properties of ultracold atoms in\nanisotropic 2D and 3D speckle potentials. In particular, we discuss the\nanisotropy of single-scattering, diffusion and localization. We also calculate\na disorder-induced shift of the energy states and propose a method to include\nit, which amounts to renormalize energies in the standard on-shell\napproximation. We show that the renormalization of energies strongly affects\nthe prediction for the 3D localization threshold (mobility edge). We illustrate\nthe theoretical findings with examples which are revelant for current matter\nwave experiments, where the disorder is created with a laser speckle. This\npaper provides a guideline for future experiments aiming at the precise\nlocation of the 3D mobility edge and study of anisotropic diffusion and\nlocalization effects in 2D and 3D.", "category": "cond-mat_dis-nn" }, { "text": "Elementary plastic events in amorphous silica: Plastic instabilities in amorphous materials are often studied using\nidealized models of binary mixtures that do not capture accurately molecular\ninteractions and bonding present in real glasses. Here we study atomic scale\nplastic instabilities in a three dimensional molecular dynamics model of silica\nglass under quasi-static shear. We identify two distinct types of elementary\nplastic events, one is a standard quasi-localized atomic rearrangement while\nthe second is a bond breaking event that is absent in simplified models of\nfragile glass formers. Our results show that both plastic events can be\npredicted by a drop of the lowest non-zero eigenvalue of the Hessian matrix\nthat vanishes at a critical strain. Remarkably, we find very high correlation\nbetween the associated eigenvectors and the non-affine displacement fields\naccompanying the bond breaking event, predicting the locus of structural\nfailure. Both eigenvectors and non-affine displacement fields display an\nEshelby-like quadrupolar structure for both failure modes, rearrangement or\nbond-breaking. Our results thus clarify the nature of atomic scale plastic\ninstabilities in silica glasses providing useful information for the\ndevelopment of mesoscale models of amorphous plasticity.", "category": "cond-mat_dis-nn" }, { "text": "Correlated Domains in Spin Glasses: We study the 3D Edwards-Anderson spin glasses, by analyzing spin-spin\ncorrelation functions in thermalized spin configurations at low T on large\nlattices. We consider individual disorder samples and analyze connected\nclusters of very correlated sites: we analyze how the volume and the surface of\nthese clusters increases with the lattice size. We qualify the important\nexcitations of the system by checking how large they are, and we define a\ncorrelation length by measuring their gyration radius. We find that the\nclusters have a very dense interface, compatible with being space filling.", "category": "cond-mat_dis-nn" }, { "text": "Probing many-body localization in a disordered quantum magnet: Quantum states cohere and interfere. Quantum systems composed of many atoms\narranged imperfectly rarely display these properties. Here we demonstrate an\nexception in a disordered quantum magnet that divides itself into nearly\nisolated subsystems. We probe these coherent clusters of spins by driving the\nsystem beyond its linear response regime at a single frequency and measuring\nthe resulting \"hole\" in the overall linear spectral response. The Fano shape of\nthe hole encodes the incoherent lifetime as well as coherent mixing of the\nlocalized excitations. For the disordered Ising magnet,\n$\\mathrm{LiHo_{0.045}Y_{0.955}F_4}$, the quality factor $Q$ for spectral holes\ncan be as high as 100,000. We tune the dynamics of the quantum degrees of\nfreedom by sweeping the Fano mixing parameter $q$ through zero via the\namplitude of the ac pump as well as a static external transverse field. The\nzero-crossing of $q$ is associated with a dissipationless response at the drive\nfrequency, implying that the off-diagonal matrix element for the two-level\nsystem also undergoes a zero-crossing. The identification of localized\ntwo-level systems in a dense and disordered dipolar-coupled spin system\nrepresents a solid state implementation of many-body localization, pushing the\nsearch forward for qubits emerging from strongly-interacting, disordered,\nmany-body systems.", "category": "cond-mat_dis-nn" }, { "text": "Novel scaling behavior of the Ising model on curved surfaces: We demonstrate the nontrivial scaling behavior of Ising models defined on (i)\na donut-shaped surface and (ii) a curved surface with a constant negative\ncurvature. By performing Monte Carlo simulations, we find that the former model\nhas two distinct critical temperatures at which both the specific heat $C(T)$\nand magnetic susceptibility $\\chi(T)$ show sharp peaks.The critical exponents\nassociated with the two critical temperatures are evaluated by the finite-size\nscaling analysis; the result reveals that the values of these exponents vary\ndepending on the temperature range under consideration. In the case of the\nlatter model, it is found that static and dynamic critical exponents deviate\nfrom those of the Ising model on a flat plane; this is a direct consequence of\nthe constant negative curvature of the underlying surface.", "category": "cond-mat_dis-nn" }, { "text": "Reply to Comment on \"Quantum Phase Transition of Randomly-Diluted\n Heisenberg Antiferromagnet on a Square Lattice\": This is a reply to the comment by A. W. Sandvik (cond-mat/0010433) on our\npaper Phys. Rev. Lett. 84, 4204 (2000). We show that his data do not conflict\nwith our data nor with our conclusions.", "category": "cond-mat_dis-nn" }, { "text": "Realization-dependent model of hopping transport in disordered media: At low injection or low temperatures, electron transport in disordered\nsemiconductors is dominated by phonon-assisted hopping between localized\nstates. A very popular approach to this hopping transport is the\nMiller-Abrahams model that requires a set of empirical parameters to define the\nhopping rates and the preferential paths between the states. We present here a\ntransport model based on the localization landscape (LL) theory in which the\nlocation of the localized states, their energies, and the coupling between them\nare computed for any specific realization, accounting for its particular\ngeometry and structure. This model unveils the transport network followed by\nthe charge carriers that essentially consists in the geodesics of a metric\ndeduced from the LL. The hopping rates and mobility are computed on a\nparadigmatic example of disordered semiconductor, and compared with the\nprediction from the actual solution of the Schr\\\"odinger equation. We explore\nthe temperature-dependency for various disorder strengths and demonstrate the\napplicability of the LL theory in efficiently modeling hopping transport in\ndisordered systems.", "category": "cond-mat_dis-nn" }, { "text": "A theory of \u03c0/2 superconducting Josephson junctions: We consider theoretically a Josephson junction with a superconducting\ncritical current density which has a random sign along the junction's surface.\nWe show that the ground state of the junction corresponds to the phase\ndifference equal to \\pi/2. Such a situation can take place in superconductor-\nferromagnet junction.", "category": "cond-mat_dis-nn" }, { "text": "Extended states in disordered systems: role of off-diagonal correlations: We study one-dimensional systems with random diagonal disorder but\noff-diagonal short-range correlations imposed by structural constraints. We\nfind that these correlations generate effective conduction channels for finite\nsystems. At a certain golden correlation condition for the hopping amplitudes,\nwe find an extended state for an infinite system. Our model has important\nimplications to charge transport in DNA molecules, and a possible set of\nexperiments in semiconductor superlattices is proposed to verify our most\ninteresting theoretical predictions.", "category": "cond-mat_dis-nn" }, { "text": "Real space Renormalization Group analysis of a non-mean field spin-glass: A real space Renormalization Group approach is presented for a non-mean field\nspin-glass. This approach has been conceived in the effort to develop an\nalternative method to the Renormalization Group approaches based on the replica\nmethod. Indeed, non-perturbative effects in the latter are quite generally out\nof control, in such a way that these approaches are non-predictive. On the\ncontrary, we show that the real space method developed in this work yields\nprecise predictions for the critical behavior and exponents of the model.", "category": "cond-mat_dis-nn" }, { "text": "Signature of ballistic effects in disordered conductors: Statistical properties of energy levels, wave functions and\nquantum-mechanical matrix elements in disordered conductors are usually\ncalculated assuming diffusive electron dynamics. Mirlin has pointed out [Phys.\nRep. 326, 259 (2000)] that ballistic effects may, under certain circumstances,\ndominate diffusive contributions. We study the influence of such ballistic\neffects on the statistical properties of wave functions in quasi-one\ndimensional disordered conductors. Our results support the view that ballistic\neffects can be significant in these systems.", "category": "cond-mat_dis-nn" }, { "text": "Democratic particle motion for meta-basin transitions in simple\n glass-formers: We use molecular dynamics computer simulations to investigate the local\nmotion of the particles in a supercooled simple liquid. Using the concept of\nthe distance matrix we find that the alpha-relaxation corresponds to a small\nnumber of crossings from one meta-basin to a neighboring one. Each crossing is\nvery rapid and involves the collective motion of O(40) particles that form a\nrelatively compact cluster, whereas string-like motions seem not to be relevant\nfor these transitions. These compact clusters are thus candidates for the\ncooperatively rearranging regions proposed long times ago by Adam and Gibbs.", "category": "cond-mat_dis-nn" }, { "text": "Resistance distance distribution in large sparse random graphs: We consider an Erdos-Renyi random graph consisting of N vertices connected by\nrandomly and independently drawing an edge between every pair of them with\nprobability c/N so that at N->infinity one obtains a graph of finite mean\ndegree c. In this regime, we study the distribution of resistance distances\nbetween the vertices of this graph and develop an auxiliary field\nrepresentation for this quantity in the spirit of statistical field theory.\nUsing this representation, a saddle point evaluation of the resistance distance\ndistribution is possible at N->infinity in terms of an 1/c expansion. The\nleading order of this expansion captures the results of numerical simulations\nvery well down to rather small values of c; for example, it recovers the\nempirical distribution at c=4 or 6 with an overlap of around 90%. At large\nvalues of c, the distribution tends to a Gaussian of mean 2/c and standard\ndeviation sqrt{2/c^3}. At small values of c, the distribution is skewed toward\nlarger values, as captured by our saddle point analysis, and many fine features\nappear in addition to the main peak, including subleading peaks that can be\ntraced back to resistance distances between vertices of specific low degrees\nand the rest of the graph. We develop a more refined saddle point scheme that\nextracts the corresponding degree-differentiated resistance distance\ndistributions. We then use this approach to recover analytically the most\napparent of the subleading peaks that originates from vertices of degree 1.\nRather intuitively, this subleading peak turns out to be a copy of the main\npeak, shifted by one unit of resistance distance and scaled down by the\nprobability for a vertex to have degree 1. We comment on a possible lack of\nsmoothness in the true N->infinity distribution suggested by the numerics.", "category": "cond-mat_dis-nn" }, { "text": "Sensitivity, Itinerancy and Chaos in Partly-Synchronized Weighted\n Networks: We present exact results, as well as some illustrative Monte Carlo\nsimulations, concerning a stochastic network with weighted connections in which\nthe fraction of nodes that are dynamically synchronized is a parameter. This\nallows one to describe from single-node kinetics to simultaneous updating of\nall the variables at each time unit. An example of the former limit is the\nwell-known sequential updating of spins in kinetic magnetic models whereas the\nlatter limit is common for updating complex cellular automata. The emergent\nbehavior changes dramatically as the parameter is varied. For small values, we\nobserved relaxation towards one of the attractors and a great sensibility to\nexternal stimuli, and for large synchronization, itinerancy as in heteroclinic\npaths among attractors; tuning the parameter in this regime, the oscillations\nwith time may abruptly change from regular to chaotic and vice versa. We show\nhow these observations, which may be relevant concerning computational\nstrategies, closely resemble some actual situations related to both searching\nand states of attention in the brain.", "category": "cond-mat_dis-nn" }, { "text": "Modelling Quasicrystal Growth: Understanding the growth of quasicrystals poses a challenging problem, not\nthe least because the quasiperiodic order present in idealized mathematical\nmodels of quasicrystals prohibit simple local growth algorithms. This can only\nbe circumvented by allowing for some degree of disorder, which of course is\nalways present in real quasicrystalline samples. In this review, we give an\noverview of the present state of theoretical research, addressing the problems,\nthe different approaches and the results obtained so far.", "category": "cond-mat_dis-nn" }, { "text": "Electric field induced memory and aging effects in pure solid N_2: We report combined high sensitivity dielectric constant and heat capacity\nmeasurements of pure solid N_2 in the presence of a small external ac electric\nfield in the audio frequency range. We have observed strong field induced aging\nand memory effects which show that field cooled samples may be prepared in a\nvariety of metastable states leading to a free energy landscape with\nexperimentally ``tunable'' barriers, and tunneling between these states may\noccur within laboratory time scales.", "category": "cond-mat_dis-nn" }, { "text": "Criterion for the occurrence of many body localization in the presence\n of a single particle mobility edge: Non-interacting fermions in one dimension can undergo a\nlocalization-delocalization transition in the presence of a quasi-periodic\npotential as a function of that potential. In the presence of interactions,\nthis transition transforms into a Many-Body Localization (MBL) transition.\nRecent studies have suggested that this type of transition can also occur in\nmodels with quasi-periodic potentials that possess single particle mobility\nedges. Two such models were studied in PRL 115,230401(2015) but only one was\nfound to exhibit an MBL transition in the presence of interactions while the\nother one did not. In this work we investigate the occurrence of MBL in the\npresence of weak interactions in five different models with single particle\nmobility edges in one dimension with a view to obtaining a criterion for the\nsame. We find that not all such models undergo a thermal-MBL phase transition\nin presence of weak interactions. We propose a criterion to determine whether\nMBL is likely to occur in presence of interaction based only on the properties\nof the non-interacting models. The relevant quantity $\\epsilon$ is a measure of\nhow localized the localized states are relative to how delocalized the\ndelocalized states are in the non-interacting model. We also study various\nother features of the non-interacting models such as the divergence of the\nlocalization length at the mobility edge and the presence or absence of\n`ergodicity' and localization in their many-body eigenstates. However, we find\nthat these features cannot be used to predict the occurrence of MBL upon the\nintroduction of weak interactions.", "category": "cond-mat_dis-nn" }, { "text": "Numerical evidences of a universal critical behavior of 2D and 3D random\n quantum clock and Potts models: The random quantum $q$-state clock and Potts models are studied in 2 and 3\ndimensions. The existence of Griffiths phases is tested in the 2D case with\n$q=6$ by sampling the integrated probability distribution of local\nsusceptibilities of the equivalent McCoy-Wu 3D classical modelswith Monte Carlo\nsimulations. No Griffiths phase is found for the clock model. In contrast,\nnumerical evidences of the existence of Griffiths phases in the random Potts\nmodel are given and the Finite Size effects are analyzed. The critical point of\nthe random quantum clock model is then studied by Strong-Disorder\nRenormalization Group. Despite a chaotic behavior of the Renormalization-Group\nflow at weak disorder, evidences are given that this critical behavior is\ngoverned by the same Infinite-Disorder Fixed Point as the Potts model,\nindependently from the number of states $q$.", "category": "cond-mat_dis-nn" }, { "text": "Absence of disordered Thouless pumps at finite frequency: A Thouless pump is a slowly driven one-dimensional band insulator which pumps\ncharge at a quantised rate. Previous work showed that pumping persists in\nweakly disordered chains, and separately in clean chains at finite drive\nfrequency. We study the interplay of disorder and finite frequency, and show\nthat the pump rate always decays to zero due to non-adiabatic transitions\nbetween the instantaneous eigenstates. However, the decay is slow, occurring on\na time-scale that is exponentially large in the period of the drive. In the\nadiabatic limit, the band gap in the instantaneous spectrum closes at a\ncritical disorder strength above which pumping ceases. We predict the scaling\nof the pump rate around this transition from a model of scattering between rare\nstates near the band edges. Our predictions can be experimentally tested in\nultracold atomic and photonic platforms.", "category": "cond-mat_dis-nn" }, { "text": "Frequency propagation: Multi-mechanism learning in nonlinear physical\n networks: We introduce frequency propagation, a learning algorithm for nonlinear\nphysical networks. In a resistive electrical circuit with variable resistors,\nan activation current is applied at a set of input nodes at one frequency, and\nan error current is applied at a set of output nodes at another frequency. The\nvoltage response of the circuit to these boundary currents is the superposition\nof an `activation signal' and an `error signal' whose coefficients can be read\nin different frequencies of the frequency domain. Each conductance is updated\nproportionally to the product of the two coefficients. The learning rule is\nlocal and proved to perform gradient descent on a loss function. We argue that\nfrequency propagation is an instance of a multi-mechanism learning strategy for\nphysical networks, be it resistive, elastic, or flow networks. Multi-mechanism\nlearning strategies incorporate at least two physical quantities, potentially\ngoverned by independent physical mechanisms, to act as activation and error\nsignals in the training process. Locally available information about these two\nsignals is then used to update the trainable parameters to perform gradient\ndescent. We demonstrate how earlier work implementing learning via chemical\nsignaling in flow networks also falls under the rubric of multi-mechanism\nlearning.", "category": "cond-mat_dis-nn" }, { "text": "Solvable model of a polymer in random media with long ranged disorder\n correlations: We present an exactly solvable model of a Gaussian (flexible) polymer chain\nin a quenched random medium. This is the case when the random medium obeys very\nlong range quadratic correlations. The model is solved in $d$ spatial\ndimensions using the replica method, and practically all the physical\nproperties of the chain can be found. In particular the difference between the\nbehavior of a chain that is free to move and a chain with one end fixed is\nelucidated. The interesting finding is that a chain that is free to move in a\nquadratically correlated random potential behaves like a free chain with $R^2\n\\sim L$, where $R$ is the end to end distance and $L$ is the length of the\nchain, whereas for a chain anchored at one end $R^2 \\sim L^4$. The exact\nresults are found to agree with an alternative numerical solution in $d=1$\ndimensions. The crossover from long ranged to short ranged correlations of the\ndisorder is also explored.", "category": "cond-mat_dis-nn" }, { "text": "Floquet Time Crystals: We define what it means for time translation symmetry to be spontaneously\nbroken in a quantum system, and show with analytical arguments and numerical\nsimulations that this occurs in a large class of many-body-localized driven\nsystems with discrete time-translation symmetry.", "category": "cond-mat_dis-nn" }, { "text": "Zero-temperature Glauber dynamics on small-world networks: The zero-temperature Glauber dynamics of the ferromagnetic Ising model on\nsmall-world networks, rewired from a two-dimensional square lattice, has been\nstudied by numerical simulations. For increasing disorder in finite networks,\nthe nonequilibrium dynamics becomes faster, so that the ground state is found\nmore likely. For any finite value of the rewiring probability p, the likelihood\nof reaching the ground state goes to zero in the thermodynamic limit, similarly\nto random networks. The spin correlation xi(r) is found to decrease with\ndistance as xi(r) ~ exp(-r/lambda), lambda being a correlation length scaling\nwith p as lambda ~ p^(-0.73). These results are compared with those obtained\nearlier for addition-type small world networks.", "category": "cond-mat_dis-nn" }, { "text": "Scaling the alpha-relaxation time of supercooled fragile organic liquids: It was shown recently that the structural alpha-relaxation time tau of\nsupercooled o-terphenyl depends on a single control parameter Gamma, which is\nthe product of a function of density E(ro), by the inverse temperature T -1. We\nextend this finding to other fragile glassforming liquids using\nlight-scattering data. Available experimental results do not allow to\ndiscriminate between several analytical forms of the function E(ro), the\nscaling arising from the separation of density and temperature in Gamma. We\nalso propose a simple form for tau(Gamma), which depends only on three\nmaterial-dependent parameters, reproducing relaxation times over 12 orders of\nmagnitude.", "category": "cond-mat_dis-nn" }, { "text": "Rare region effects and dynamics near the many-body localization\n transition: The low-frequency response of systems near the many-body localization phase\ntransition, on either side of the transition, is dominated by contributions\nfrom rare regions that are locally \"in the other phase\", i.e., rare localized\nregions in a system that is typically thermal, or rare thermal regions in a\nsystem that is typically localized. Rare localized regions affect the\nproperties of the thermal phase, especially in one dimension, by acting as\nbottlenecks for transport and the growth of entanglement, whereas rare thermal\nregions in the localized phase act as local \"baths\" and dominate the\nlow-frequency response of the MBL phase. We review recent progress in\nunderstanding these rare-region effects, and discuss some of the open questions\nassociated with them: in particular, whether and in what circumstances a single\nrare thermal region can destabilize the many-body localized phase.", "category": "cond-mat_dis-nn" }, { "text": "Human Genome data analyzed by an evolutionary method suggests a decrease\n in cerebral protein-synthesis rate as cause of schizophrenia and an increase\n as antipsychotic mechanism: The Human Genome Project (HGP) provides researchers with the data of nearly\nall human genes and the challenge to use this information for elucidating the\netiology of common disorders. A secondary Darwinian method was applied to HGP\nand other research data to approximate and possibly unravel the etiology of\nschizophrenia. The results indicate that genetic and epigenetic variants of\ngenes involved in signal transduction, transcription and translation -\nconverging at the protein-synthesis rate (PSR) as common final pathway - might\nbe responsible for the genetic susceptibility to schizophrenia. Environmental\n(e.g. viruses)and/or genetic factors can lead to cerebral PSR (CPSR)\ndeficiency. The CPSR hypothesis of schizophrenia and antipsychotic mechanism\nexplains 96% of the major facts of schizophrenia, reveals links between\npreviously unrelated facts, integrates many hypotheses, and implies that\nschizophrenia should be easily preventable and treatable, partly by\nimmunization against neurotrophic viruses and partly by the development of new\ndrugs which selectively increase CPSR. Part of the manuscript has been\npublished in a modified form as \"The glial growth factors deficiency and\nsynaptic destabilization hypothesis of schizophrenia\" in BMC Psychiatry\navailable online at http://www.biomedcentral.com/1471-244X/2/8/", "category": "cond-mat_dis-nn" }, { "text": "Critical-to-Insulator Transitions and Fractality Edges in Perturbed\n Flatbands: We study the effect of quasiperiodic perturbations on one-dimensional\nall-bands-flat lattice models. Such networks can be diagonalized by a finite\nsequence of local unitary transformations parameterized by angles $\\theta_i$.\nWithout loss of generality, we focus on the case of two bands with bandgap\n$\\Delta$. Weak perturbations lead to an effective Hamiltonian with both on- and\noff-diagonal quasiperiodic terms that depend on $\\theta_i$. For some angle\nvalues, the effective model coincides with the extended Harper model. By\nvarying the parameters of the quasiperiodic potentials, \\iffalse and the\nmanifold angles $\\theta_i$ \\fi we observe localized insulating states and an\nentire parameter range hosting critical states with subdiffusive transport. For\nfinite quasiperiodic potential strength, the critical-to-insulating transition\nbecomes energy dependent with what we term fractality edges separating\nlocalized from critical states.", "category": "cond-mat_dis-nn" }, { "text": "Dynamic entropies, long-range correlations, and fluctuations in complex\n linear structures: We investigate symbolic sequences and in particular information carriers as\ne.g. books and DNA-strings. First the higher order Shannon entropies are\ncalculated, a characteristic root law is detected. Then the algorithmic entropy\nis estimated by using Lempel-Ziv compression algorithms. In the third section\nthe correlation function for distant letters, the low frequency Fourier\nspectrum and the characteristic scaling exponents are calculated. We show that\nall these measures are able to detect long-range correlations. However, as\ndemonstrated by shuffling experiments, different measures operate on different\nlength scales. The longest correlations found in our analysis comprise a few\nhundreds or thousands of letters and may be understood as long-wave\nfluctuations of the composition.", "category": "cond-mat_dis-nn" }, { "text": "Flat bands in fractal-like geometry: We report the presence of multiple flat bands in a class of two-dimensional\n(2D) lattices formed by Sierpinski gasket (SPG) fractal geometries as the basic\nunit cells. Solving the tight-binding Hamiltonian for such lattices with\ndifferent generations of a SPG network, we find multiple degenerate and\nnon-degenerate completely flat bands, depending on the configuration of\nparameters of the Hamiltonian. Moreover, we find a generic formula to determine\nthe number of such bands as a function of the generation index $\\ell$ of the\nfractal geometry. We show that the flat bands and their neighboring dispersive\nbands have remarkable features, the most interesting one being the spin-1\nconical-type spectrum at the band center without any staggered magnetic flux,\nin contrast to the Kagome lattice. We furthermore investigate the effect of the\nmagnetic flux in these lattice settings and show that different combinations of\nfluxes through such fractal unit cells lead to richer spectrum with a single\nisolated flat band or gapless electron- or hole-like flat bands. Finally, we\ndiscuss a possible experimental setup to engineer such fractal flat band\nnetwork using single-mode laser-induced photonic waveguides.", "category": "cond-mat_dis-nn" }, { "text": "Localization in Correlated Bi-Layer Structures: From Photonic Cristals\n to Metamaterials and Electron Superlattices: In a unified approach, we study the transport properties of\nperiodic-on-average bi-layered photonic crystals, metamaterials and electron\nsuperlattices. Our consideration is based on the analytical expression for the\nlocalization length derived for the case of weakly fluctuating widths of\nlayers, that also takes into account possible correlations in disorder. We\nanalyze how the correlations lead to anomalous properties of transport. In\nparticular, we show that for quarter stack layered media specific correlations\ncan result in a $\\omega^2$-dependence of the Lyapunov exponent in all spectral\nbands.", "category": "cond-mat_dis-nn" }, { "text": "Random Defect Lines in Conformal Minimal Models: We analyze the effect of adding quenched disorder along a defect line in the\n2D conformal minimal models using replicas. The disorder is realized by a\nrandom applied magnetic field in the Ising model, by fluctuations in the\nferromagnetic bond coupling in the Tricritical Ising model and Tricritical\nThree-state Potts model (the $\\phi_{12}$ operator), etc.. We find that for the\nIsing model, the defect renormalizes to two decoupled half-planes without\ndisorder, but that for all other models, the defect renormalizes to a\ndisorder-dominated fixed point. Its critical properties are studied with an\nexpansion in $\\eps \\propto 1/m$ for the mth Virasoro minimal model. The decay\nexponents $X_N=\\frac{N}{2}(1-\\frac{9(3N-4)}{4(m+1)^2}+\n\\mathcal{O}(\\frac{3}{m+1})^3)$ of the Nth moment of the two-point function of\n$\\phi_{12}$ along the defect are obtained to 2-loop order, exhibiting\nmultifractal behavior.This leads to a typical decay exponent $X_{\\rm typ}={1/2}\n(1+\\frac{9}{(m+1)^2}+\\mathcal{O}(\\frac{3}{m+1})^3)$. One-point functions are\nseen to have a non-self-averaging amplitude. The boundary entropy is larger\nthan that of the pure system by order 1/m^3.\n As a byproduct of our calculations, we also obtain to 2-loop order the\nexponent $\\tilde{X}_N=N(1-\\frac{2}{9\\pi^2}(3N-4)(q-2)^2+\\mathcal{O}(q-2)^3)$ of\nthe Nth moment of the energy operator in the q-state Potts model with bulk bond\ndisorder.", "category": "cond-mat_dis-nn" }, { "text": "Simulating Spin Waves in Entropy Stabilized Oxides: The entropy stabilized oxide\nMg$_{0.2}$Co$_{0.2}$Ni$_{0.2}$Cu$_{0.2}$Zn$_{0.2}$O exhibits antiferromagnetic\norder and magnetic excitations, as revealed by recent neutron scattering\nexperiments. This observation raises the question of the nature of spin wave\nexcitations in such disordered systems. Here, we investigate theoretically the\nmagnetic ground state and the spin-wave excitations using linear spin-wave\ntheory in combination with the supercell approximation to take into account the\nextreme disorder in this magnetic system. We find that the experimentally\nobserved antiferromagnetic structure can be stabilized by a rhombohedral\ndistortion together with large second nearest neighbor interactions. Our\ncalculations show that the spin-wave spectrum consists of a well-defined\nlow-energy coherent spectrum in the background of an incoherent continuum that\nextends to higher energies.", "category": "cond-mat_dis-nn" }, { "text": "Chain breaking and Kosterlitz-Thouless scaling at the many-body\n localization transition in the random field Heisenberg spin chain: Despite tremendous theoretical efforts to understand subtleties of the\nmany-body localization (MBL) transition, many questions remain open, in\nparticular concerning its critical properties. Here we make the key observation\nthat MBL in one dimension is accompanied by a spin freezing mechanism which\ncauses chain breakings in the thermodynamic limit. Using analytical and\nnumerical approaches, we show that such chain breakings directly probe the\ntypical localization length, and that their scaling properties at the MBL\ntransition agree with the Kosterlitz-Thouless scenario predicted by\nphenomenological renormalization group approaches.", "category": "cond-mat_dis-nn" }, { "text": "Many-body localization transition in a frustrated XY chain: We demonstrate many-body localization (MBL) transition in a one-dimensional\nisotropic XY chain with a weak next-nearest-neighbor frustration in a random\nmagnetic field. We perform finite-size exact diagonalization calculations of\nlevel-spacing statistics and fractal dimensions to characterize the MBL\ntransition with increasing the random field amplitude. An equivalent\nrepresentation of the model in terms of spinless fermions explains the presence\nof the delocalized phase by the appearance of an effective non-local\ninteraction between the fermions. This interaction appears due to frustration\nprovided by the next-nearest-neighbor hopping.", "category": "cond-mat_dis-nn" }, { "text": "Potts spin glasses with 3, 4 and 5 states near $T=T_c$: expanding around\n the replica symmetric solution: Expansion for the free energy functionals of the Potts spin glass models with\n3, 4 and 5 states up to the fourth order in $\\delta q_{\\alpha \\beta }$ around\nthe replica symmetric solution (RS) is investigated using a special\nquadrupole-like representation. The temperature dependence of the 1RSB order\nparameters is obtained in the vicinity of the point $T=T_c$ where the RS\nsolution becomes unstable. The crossover from continuous to jumpwise behavior\nwith increasing of number of states is derived analytically. The comparison is\nmade of the free energy expansion for the Potts spin glass with that for other\nmodels.", "category": "cond-mat_dis-nn" }, { "text": "Clustering of solutions in the symmetric binary perceptron: The geometrical features of the (non-convex) loss landscape of neural network\nmodels are crucial in ensuring successful optimization and, most importantly,\nthe capability to generalize well. While minimizers' flatness consistently\ncorrelates with good generalization, there has been little rigorous work in\nexploring the condition of existence of such minimizers, even in toy models.\nHere we consider a simple neural network model, the symmetric perceptron, with\nbinary weights. Phrasing the learning problem as a constraint satisfaction\nproblem, the analogous of a flat minimizer becomes a large and dense cluster of\nsolutions, while the narrowest minimizers are isolated solutions. We perform\nthe first steps toward the rigorous proof of the existence of a dense cluster\nin certain regimes of the parameters, by computing the first and second moment\nupper bounds for the existence of pairs of arbitrarily close solutions.\nMoreover, we present a non rigorous derivation of the same bounds for sets of\n$y$ solutions at fixed pairwise distances.", "category": "cond-mat_dis-nn" }, { "text": "Mechanical Failure in Amorphous Solids: Scale Free Spinodal Criticality: The mechanical failure of amorphous media is a ubiquitous phenomenon from\nmaterial engineering to geology. It has been noticed for a long time that the\nphenomenon is \"scale-free\", indicating some type of criticality. In spite of\nattempts to invoke \"Self-Organized Criticality\", the physical origin of this\ncriticality, and also its universal nature, being quite insensitive to the\nnature of microscopic interactions, remained elusive. Recently we proposed that\nthe precise nature of this critical behavior is manifested by a spinodal point\nof a thermodynamic phase transition. Moreover, at the spinodal point there\nexists a divergent correlation length which is associated with the\nsystem-spanning instabilities (known also as shear bands) which are typical to\nthe mechanical yield. Demonstrating this requires the introduction of an \"order\nparameter\" that is suitable for distinguishing between disordered amorphous\nsystems, and an associated correlation function, suitable for picking up the\ngrowing correlation length. The theory, the order parameter, and the\ncorrelation functions used are universal in nature and can be applied to any\namorphous solid that undergoes mechanical yield. Critical exponents for the\ncorrelation length divergence and the system size dependence are estimated. The\nphenomenon is seen at its sharpest in athermal systems, as is explained below;\nin this paper we extend the discussion also to thermal systems, showing that at\nsufficiently high temperatures the spinodal phenomenon is destroyed by thermal\nfluctuations.", "category": "cond-mat_dis-nn" }, { "text": "Short-time critical dynamics of the three-dimensional systems with\n long-range correlated disorder: Monte Carlo simulations of the short-time dynamic behavior are reported for\nthree-dimensional Ising and XY models with long-range correlated disorder at\ncriticality, in the case corresponding to linear defects. The static and\ndynamic critical exponents are determined for systems starting separately from\nordered and disordered initial states. The obtained values of the exponents are\nin a good agreement with results of the field-theoretic description of the\ncritical behavior of these models in the two-loop approximation and with our\nresults of Monte Carlo simulations of three-dimensional Ising model in\nequilibrium state.", "category": "cond-mat_dis-nn" }, { "text": "Odor recognition and segmentation by a model olfactory bulb and cortex: We present a model of an olfactory system that performs odor segmentation.\nBased on the anatomy and physiology of natural olfactory systems, it consists\nof a pair of coupled modules, bulb and cortex. The bulb encodes the odor inputs\nas oscillating patterns. The cortex functions as an associative memory: When\nthe input from the bulb matches a pattern stored in the connections between its\nunits, the cortical units resonate in an oscillatory pattern characteristic of\nthat odor. Further circuitry transforms this oscillatory signal to a\nslowly-varying feedback to the bulb. This feedback implements olfactory\nsegmentation by suppressing the bulbar response to the pre-existing odor,\nthereby allowing subsequent odors to be singled out for recognition.", "category": "cond-mat_dis-nn" }, { "text": "Neutron Scattering Study of Fluctuating and Static Spin Correlations in\n the Anisotropic Spin Glass Fe$_2$TiO$_5$: The anisotropic spin glass transition, in which spin freezing is observed\nonly along the c-axis in pseudobrookite Fe$_2$TiO$_5$, has long been perplexing\nbecause the Fe$^{3+}$ moments (d$^5$) are expected to be isotropic. Recently,\nneutron diffraction demonstrated that surfboard-shaped antiferromagnetic\nnanoregions coalesce above the glass transition temperature, T$_g$ $\\approx$ 55\nK, and a model was proposed in which the freezing of the fluctuations of the\nsurfboards' magnetization leads to the anisotropic spin glass state. Given this\nnew model, we have carried out high resolution inelastic neutron scattering\nmeasurements of the spin-spin correlations to understand the temperature\ndependence of the intra-surfboard spin dynamics on neutron (picosecond)\ntime-scales. Here, we report on the temperature-dependence of the spin\nfluctuations measured from single crystal Fe$_2$TiO$_5$. Strong quasi-elastic\nmagnetic scattering, arising from intra-surfboard correlations, is observed\nwell above T$_g$. The spin fluctuations possess a steep energy-wave vector\nrelation and are indicative of strong exchange interactions, consistent with\nthe large Curie-Weiss temperature. As the temperature approaches T$_g$ from\nabove, a shift in spectral weight from inelastic to elastic scattering is\nobserved. At various temperatures between 4 K and 300 K, a characteristic\nrelaxation rate of the fluctuations is determined. Despite the freezing of the\nmajority of the spin correlations, an inelastic contribution remains even at\nbase temperature, signifying the presence of fluctuating intra-surfboard spin\ncorrelations to at least T/T$_g$ $\\approx$ 0.1 consistent with a description of\nFe$_2$TiO$_5$ as a hybrid between conventional and geometrically frustrated\nspin glasses.", "category": "cond-mat_dis-nn" }, { "text": "Transverse confinement of ultrasound through the Anderson transition in\n 3D mesoglasses: We report an in-depth investigation of the Anderson localization transition\nfor classical waves in three dimensions (3D). Experimentally, we observe clear\nsignatures of Anderson localization by measuring the transverse confinement of\ntransmitted ultrasound through slab-shaped mesoglass samples. We compare our\nexperimental data with predictions of the self-consistent theory of Anderson\nlocalization for an open medium with the same geometry as our samples. This\nmodel describes the transverse confinement of classical waves as a function of\nthe localization (correlation) length, $\\xi$ ($\\zeta$), and is fitted to our\nexperimental data to quantify the transverse spreading/confinement of\nultrasound all of the way through the transition between diffusion and\nlocalization. Hence we are able to precisely identify the location of the\nmobility edges at which the Anderson transitions occur.", "category": "cond-mat_dis-nn" }, { "text": "Delays, connection topology, and synchronization of coupled chaotic maps: We consider networks of coupled maps where the connections between units\ninvolve time delays. We show that, similar to the undelayed case, the\nsynchronization of the network depends on the connection topology,\ncharacterized by the spectrum of the graph Laplacian. Consequently, scale-free\nand random networks are capable of synchronizing despite the delayed flow of\ninformation, whereas regular networks with nearest-neighbor connections and\ntheir small-world variants generally exhibit poor synchronization. On the other\nhand, connection delays can actually be conducive to synchronization, so that\nit is possible for the delayed system to synchronize where the undelayed system\ndoes not. Furthermore, the delays determine the synchronized dynamics, leading\nto the emergence of a wide range of new collective behavior which the\nindividual units are incapable of producing in isolation.", "category": "cond-mat_dis-nn" }, { "text": "Effect of weak disorder in the Fully Frustrated XY model: The critical behaviour of the Fully Frustrated XY model in presence of weak\npositional disorder is studied in a square lattice by Monte Carlo methods. The\ncritical exponent associated to the divergence of the chiral correlation length\nis found to be equal to 1.7 already at very small values of disorder.\nFurthermore the helicity modulus jump is found larger than the universal value\nexpected in the XY model.", "category": "cond-mat_dis-nn" }, { "text": "Zero-Temperature Dynamics of Plus/Minus J Spin Glasses and Related\n Models: We study zero-temperature, stochastic Ising models sigma(t) on a\nd-dimensional cubic lattice with (disordered) nearest-neighbor couplings\nindependently chosen from a distribution mu on R and an initial spin\nconfiguration chosen uniformly at random. Given d, call mu type I (resp., type\nF) if, for every x in the lattice, sigma(x,t) flips infinitely (resp., only\nfinitely) many times as t goes to infinity (with probability one) --- or else\nmixed type M. Models of type I and M exhibit a zero-temperature version of\n``local non-equilibration''. For d=1, all types occur and the type of any mu is\neasy to determine. The main result of this paper is a proof that for d=2,\nplus/minus J models (where each coupling is independently chosen to be +J with\nprobability alpha and -J with probability 1-alpha) are type M, unlike\nhomogeneous models (type I) or continuous (finite mean) mu's (type F). We also\nprove that all other noncontinuous disordered systems are type M for any d\ngreater than or equal to 2. The plus/minus J proof is noteworthy in that it is\nmuch less ``local'' than the other (simpler) proof. Homogeneous and plus/minus\nJ models for d greater than or equal to 3 remain an open problem.", "category": "cond-mat_dis-nn" }, { "text": "Extensive eigenvalues in spin-spin correlations: a tool for counting\n pure states in Ising spin glasses: We study the nature of the broken ergodicity in the low temperature phase of\nIsing spin glass systems, using as a diagnostic tool the spectrum of\neigenvalues of the spin-spin correlation function. We show that multiple\nextensive eigenvalues of the correlation matrix $C_{ij}\\equiv< S_i S_j>$ occur\nif and only if there is replica symmetry breaking. We support our arguments\nwith Exchange Monte-Carlo results for the infinite-range problem. Here we find\nmultiple extensive eigenvalues in the RSB phase for $N \\agt 200$, but only a\nsingle extensive eigenvalue for phases with long-range order but no RSB.\nNumerical results for the short range model in four spatial dimensions, for\n$N\\le 1296$, are consistent with the presence of a single extensive eigenvalue,\nwith the subdominant eigenvalue behaving in agreement with expectations derived\nfrom the droplet model. Because of the small system sizes we cannot exclude the\npossibility of replica symmetry breaking with finite size corrections in this\nregime.", "category": "cond-mat_dis-nn" }, { "text": "Entanglement and localization in long-range quadratic Lindbladians: Existence of Anderson localization is considered a manifestation of coherence\nof classical and quantum waves in disordered systems. Signatures of\nlocalization have been observed in condensed matter and cold atomic systems\nwhere the coupling to the environment can be significantly suppressed but not\neliminated. In this work we explore the phenomena of localization in random\nLindbladian dynamics describing open quantum systems. We propose a model of\none-dimensional chain of non-interacting, spinless fermions coupled to a local\nensemble of baths. The jump operator mediating the interaction with the bath\nlinked to each site has a power-law tail with an exponent $p$. We show that the\nsteady state of the system undergoes a localization entanglement phase\ntransition by tuning $p$ which remains stable in the presence of coherent\nhopping. Unlike the entanglement transition in the quantum trajectories of open\nsystems, this transition is exhibited by the averaged steady state density\nmatrix of the Lindbladian. The steady state in the localized phase is\ncharacterised by a heterogeneity in local population imbalance, while the jump\noperators exhibit a constant participation ratio of the sites they affect. Our\nwork provides a novel realisation of localization physics in open quantum\nsystems.", "category": "cond-mat_dis-nn" }, { "text": "Spontaneous ordering against an external field in nonequilibrium systems: We study the collective behavior of nonequilibrium systems subject to an\nexternal field with a dynamics characterized by the existence of\nnon-interacting states. Aiming at exploring the generality of the results, we\nconsider two types of models according to the nature of their state variables:\n(i) a vector model, where interactions are proportional to the overlap between\nthe states, and (ii) a scalar model, where interaction depends on the distance\nbetween states. In both cases the system displays three phases: two ordered\nphases, one parallel to the field, and another orthogonal to the field; and a\ndisordered phase. The phase space is numerically characterized for each model\nin a fully connected network. By placing the particles on a small-world\nnetwork, we show that, while a regular lattice favors the alignment with the\nfield, the presence of long-range interactions promotes the formation of the\nordered phase orthogonal to the field.", "category": "cond-mat_dis-nn" }, { "text": "Unsupervised learning of phase transitions via modified anomaly\n detection with autoencoders: In this paper, a modified method of anomaly detection using convolutional\nautoencoders is employed to predict phase transitions in several statistical\nmechanical models on a square lattice. We show that, when the autoencoder is\ntrained with input data of various phases, the mean-square-error loss function\ncan serve as a measure of disorder, and its standard deviation becomes an\nexcellent indicator of critical points. We find that various types of phase\ntransition points, including first-order, second-order, and topological ones,\ncan be faithfully detected by the peaks in the standard deviation of the loss\nfunction. Besides, the values of transition points can be accurately determined\nunder the analysis of finite-size scaling. Our results demonstrate that the\npresent approach has general application in identification/classification of\nphase transitions even without a priori knowledge of the systems in question.", "category": "cond-mat_dis-nn" }, { "text": "Effect of connecting wires on the decoherence due to electron-electron\n interaction in a metallic ring: We consider the weak localization in a ring connected to reservoirs through\nleads of finite length and submitted to a magnetic field. The effect of\ndecoherence due to electron-electron interaction on the harmonics of AAS\noscillations is studied, and more specifically the effect of the leads. Two\nresults are obtained for short and long leads regimes. The scale at which the\ncrossover occurs is discussed. The long leads regime is shown to be more\nrealistic experimentally.", "category": "cond-mat_dis-nn" }, { "text": "Spin Domains Generate Hierarchical Ground State Structure in J=+/-1 Spin\n Glasses: Unbiased samples of ground states were generated for the short-range Ising\nspin glass with Jij=+/-1, in three dimensions. Clustering the ground states\nrevealed their hierarchical structure, which is explained by correlated spin\ndomains, serving as cores for macroscopic zero energy \"excitations\".", "category": "cond-mat_dis-nn" }, { "text": "Filling a silo with a mixture of grains: Friction-induced segregation: We study the filling process of a two-dimensional silo with inelastic\nparticles by simulation of a granular media lattice gas (GMLG) model. We\ncalculate the surface shape and flow profiles for a monodisperse system and we\nintroduce a novel generalization of the GMLG model for a binary mixture of\nparticles of different friction properties where, for the first time, we\nmeasure the segregation process on the surface. The results are in good\nagreement with a recent theory, and we explain the observed small deviations by\nthe nonuniform velocity profile.", "category": "cond-mat_dis-nn" }, { "text": "Zero-modes in the random hopping model: If the number of lattice sites is odd, a quantum particle hopping on a\nbipartite lattice with random hopping between the two sublattices only is\nguaranteed to have an eigenstate at zero energy. We show that the localization\nlength of this eigenstate depends strongly on the boundaries of the lattice,\nand can take values anywhere between the mean free path and infinity. The same\ndependence on boundary conditions is seen in the conductance of such a lattice\nif it is connected to electron reservoirs via narrow leads. For any nonzero\nenergy, the dependence on boundary conditions is removed for sufficiently large\nsystem sizes.", "category": "cond-mat_dis-nn" }, { "text": "Thermodynamic picture of the glassy state gained from exactly solvable\n models: A picture for thermodynamics of the glassy state was introduced recently by\nus (Phys. Rev. Lett. {\\bf 79} (1997) 1317; {\\bf 80} (1998) 5580). It starts by\nassuming that one extra parameter, the effective temperature, is needed to\ndescribe the glassy state. This approach connects responses of macroscopic\nobservables to a field change with their temporal fluctuations, and with the\nfluctuation-dissipation relation, in a generalized, non-equilibrium way.\nSimilar universal relations do not hold between energy fluctuations and the\nspecific heat.\n In the present paper the underlying arguments are discussed in greater\nlength. The main part of the paper involves details of the exact dynamical\nsolution of two simple models introduced recently: uncoupled harmonic\noscillators subject to parallel Monte Carlo dynamics, and independent spherical\nspins in a random field with such dynamics. At low temperature the relaxation\ntime of both models diverges as an Arrhenius law, which causes glassy behavior\nin typical situations. In the glassy regime we are able to verify the above\nmentioned relations for the thermodynamics of the glassy state.\n In the course of the analysis it is argued that stretched exponential\nbehavior is not a fundamental property of the glassy state, though it may be\nuseful for fitting in a limited parameter regime.", "category": "cond-mat_dis-nn" }, { "text": "Information Bounds on phase transitions in disordered systems: Information theory, rooted in computer science, and many-body physics, have\ntraditionally been studied as (almost) independent fields. Only recently has\nthis paradigm started to shift, with many-body physics being studied and\ncharacterized using tools developed in information theory. In our work, we\nintroduce a new perspective on this connection, and study phase transitions in\nmodels with randomness, such as localization in disordered systems, or random\nquantum circuits with measurements. Utilizing information-based arguments\nregarding probability distribution differentiation, we bound critical exponents\nin such phase transitions (specifically, those controlling the correlation or\nlocalization lengths). We benchmark our method and rederive the well-known\nHarris criterion, bounding critical exponents in the Anderson localization\ntransition for noninteracting particles, as well as classical disordered spin\nsystems. We then move on to apply our method to many-body localization. While\nin real space our critical exponent bound agrees with recent consensus, we find\nthat, somewhat surprisingly, numerical results on Fock-space localization for\nlimited-sized systems do not obey our bounds, indicating that the simulation\nresults might not hold asymptotically (similarly to what is now believed to\nhave occurred in the real-space problem). We also apply our approach to random\nquantum circuits with random measurements, for which we can derive bounds\ntranscending recent mappings to percolation problems.", "category": "cond-mat_dis-nn" }, { "text": "Impact of boundaries on fully connected random geometric networks: Many complex networks exhibit a percolation transition involving a\nmacroscopic connected component, with universal features largely independent of\nthe microscopic model and the macroscopic domain geometry. In contrast, we show\nthat the transition to full connectivity is strongly influenced by details of\nthe boundary, but observe an alternative form of universality. Our approach\ncorrectly distinguishes connectivity properties of networks in domains with\nequal bulk contributions. It also facilitates system design to promote or avoid\nfull connectivity for diverse geometries in arbitrary dimension.", "category": "cond-mat_dis-nn" }, { "text": "Metallic spin-glasses beyond mean-field: An approach to the\n impurity-concentration dependence of the freezing temperature: A relation between the freezing temperature ($T^{}_{\\rm g}$) and the exchange\ncouplings ($J^{}_{ij}$) in metallic spin-glasses is derived, taking the\nspin-correlations ($G^{}_{ij}$) into account. This approach does not involve a\ndisorder-average. The expansion of the correlations to first order in\n$J^{}_{ij}/T^{}_{\\rm g}$ leads to the molecular-field result from\nThouless-Anderson-Palmer. Employing the current theory of the spin-interaction\nin disordered metals, an equation for $T^{}_{\\rm g}$ as a function of the\nconcentration of impurities is obtained, which reproduces the available data\nfrom {\\sl Au}Fe, {\\sl Ag}Mn, and {\\sl Cu}Mn alloys well.", "category": "cond-mat_dis-nn" }, { "text": "Finite Temperature Ordering in the Three-Dimensional Gauge Glass: We present results of Monte Carlo simulations of the gauge glass model in\nthree dimensions using exchange Monte Carlo. We show for the first time clear\nevidence of the vortex glass ordered phase at finite temperature. Using finite\nsize scaling we obtain estimates for the correlation length exponent, nu = 1.39\n+/- 0.20, the correlation function exponent, eta = -0.47 +/- 0.07, and the\ndynamic exponent z = 4.2 +/- 0.6. Using our values for z and nu we calculate\nthe resistivity exponent to be s = 4.5 +/- 1.1. Finally, we provide a plausible\nlower bound on the the zero-temperature stiffness exponent, theta >= 0.18.", "category": "cond-mat_dis-nn" }, { "text": "Saddles and dynamics in a solvable mean-field model: We use the saddle-approach, recently introduced in the numerical\ninvestigation of simple model liquids, in the analysis of a mean-field solvable\nsystem. The investigated system is the k-trigonometric model, a k-body\ninteraction mean field system, that generalizes the trigonometric model\nintroduced by Madan and Keyes [J. Chem. Phys. 98, 3342 (1993)] and that has\nbeen recently introduced to investigate the relationship between thermodynamics\nand topology of the configuration space. We find a close relationship between\nthe properties of saddles (stationary points of the potential energy surface)\nvisited by the system and the dynamics. In particular the temperature\ndependence of saddle order follows that of the diffusivity, both having an\nArrhenius behavior at low temperature and a similar shape in the whole\ntemperature range. Our results confirm the general usefulness of the\nsaddle-approach in the interpretation of dynamical processes taking place in\ninteracting systems.", "category": "cond-mat_dis-nn" }, { "text": "Random Ising chain in transverse and longitudinal fields: Strong\n disorder RG study: Motivated by the compound ${\\rm LiHo}_x{\\rm Y}_{1-x}{\\rm F}_4$, we consider\nthe Ising chain with random couplings and in the presence of simultaneous\nrandom transverse and longitudinal fields, and study its low-energy properties\nat zero temperature by the strong disorder renormalization group approach. In\nthe absence of longitudinal fields, the system exhibits a quantum-ordered and a\nquantum-disordered phase separated by a critical point of infinite disorder.\nWhen the longitudinal random field is switched on, the ordered phase vanishes\nand the trajectories of the renormalization group are attracted to two\ndisordered fixed points: one is characteristic of the classical random field\nIsing chain, the other describes the quantum disordered phase. The two\ndisordered phases are separated by a separatrix that starts at the infinite\ndisorder fixed point and near which there are strong quantum fluctuations.", "category": "cond-mat_dis-nn" }, { "text": "Computing the number of metastable states in infinite-range models: In these notes I will review the results that have been obtained in these\nlast years on the computation of the number of metastable states in\ninfinite-range models of disordered systems. This is a particular case of the\nproblem of computing the exponentially large number of stationary points of a\nrandom function. Quite surprisingly supersymmetry plays a crucial role in this\nproblem. A careful analysis of the physical implication of supersymmetry and of\nsupersymmetry breaking will be presented: the most spectacular one is that in\nthe Sherrington-Kirkpatrick model for spin glasses most of the stationary\npoints are saddles, as predicted long time ago.", "category": "cond-mat_dis-nn" }, { "text": "Dependence of critical parameters of 2D Ising model on lattice size: For the 2D Ising model, we analyzed dependences of thermodynamic\ncharacteristics on number of spins by means of computer simulations. We\ncompared experimental data obtained using the Fisher-Kasteleyn algorithm on a\nsquare lattice with $N=l{\\times}l$ spins and the asymptotic Onsager solution\n($N\\to\\infty$). We derived empirical expressions for critical parameters as\nfunctions of $N$ and generalized the Onsager solution on the case of a\nfinite-size lattice. Our analytical expressions for the free energy and its\nderivatives (the internal energy, the energy dispersion and the heat capacity)\ndescribe accurately the results of computer simulations. We showed that when\n$N$ increased the heat capacity in the critical point increased as $lnN$. We\nspecified restrictions on the accuracy of the critical temperature due to\nfinite size of our system. Also in the finite-dimensional case, we obtained\nexpressions describing temperature dependences of the magnetization and the\ncorrelation length. They are in a good qualitative agreement with the results\nof computer simulations by means of the dynamic Metropolis Monte Carlo method.", "category": "cond-mat_dis-nn" }, { "text": "Experimental Observation of Phase Transitions in Spatial Photonic Ising\n Machine: Statistical spin dynamics plays a key role to understand the working\nprinciple for novel optical Ising machines. Here we propose the gauge\ntransformations for spatial photonic Ising machine, where a single spatial\nphase modulator simultaneously encodes spin configurations and programs\ninteraction strengths. Thanks to gauge transformation, we experimentally\nevaluate the phase diagram of high-dimensional spin-glass equilibrium system\nwith $100$ fully-connected spins. We observe the presence of paramagnetic,\nferromagnetic as well as spin-glass phases and determine the critical\ntemperature $T_c$ and the critical probability ${{p}_{c}}$ of phase\ntransitions, which agree well with the mean-field theory predictions. Thus the\napproximation of the mean-field model is experimentally validated in the\nspatial photonic Ising machine. Furthermore, we discuss the phase transition in\nparallel with solving combinatorial optimization problems during the cooling\nprocess and identify that the spatial photonic Ising machine is robust with\nsufficient many-spin interactions, even when the system is associated with the\noptical aberrations and the measurement uncertainty.", "category": "cond-mat_dis-nn" }, { "text": "Ward type identities for the 2d Anderson model at weak disorder: Using the particular momentum conservation laws in dimension d=2, we can\nrewrite the Anderson model in terms of low momentum long range fields, at the\nprice of introducing electron loops. The corresponding loops satisfy a Ward\ntype identity, hence are much smaller than expected. This fact should be useful\nfor a study of the weak-coupling model in the middle of the spectrum of the\nfree Hamiltonian.", "category": "cond-mat_dis-nn" }, { "text": "Neural networks and logical reasoning systems. A translation table: A correspondence is established between the elements of logic reasoning\nsystems (knowledge bases, rules, inference and queries) and the hardware and\ndynamical operations of neural networks. The correspondence is framed as a\ngeneral translation dictionary which, hopefully, will allow to go back and\nforth between symbolic and network formulations, a desirable step in\nlearning-oriented systems and multicomputer networks. In the framework of Horn\nclause logics it is found that atomic propositions with n arguments correspond\nto nodes with n-th order synapses, rules to synaptic intensity constraints,\nforward chaining to synaptic dynamics and queries either to simple node\nactivation or to a query tensor dynamics.", "category": "cond-mat_dis-nn" }, { "text": "Disorder-Induced Vibrational Localization: The vibrational equivalent of the Anderson tight-binding Hamiltonian has been\nstudied, with particular focus on the properties of the eigenstates at the\ntransition from extended to localized states. The critical energy has been\nfound approximately for several degrees of force-constant disorder using\nsystem-size scaling of the multifractal spectra of the eigenmodes, and the\nspectrum at which there is no system-size dependence has been obtained. This is\nshown to be in good agreement with the critical spectrum for the electronic\nproblem, which has been derived both numerically and by analytic means.\nUniversality of the critical states is therefore suggested also to hold for the\nvibrational problem.", "category": "cond-mat_dis-nn" }, { "text": "Energy statistics in disordered systems: The local REM conjecture and\n beyond: Recently, Bauke and Mertens conjectured that the local statistics of energies\nin random spin systems with discrete spin space should in most circumstances be\nthe same as in the random energy model. Here we give necessary conditions for\nthis hypothesis to be true, which we show to hold in wide classes of examples:\nshort range spin glasses and mean field spin glasses of the SK type. We also\nshow that, under certain conditions, the conjecture holds even if energy levels\nthat grow moderately with the volume of the system are considered. In the case\nof the Generalised Random energy model, we give a complete analysis for the\nbehaviour of the local energy statistics at all energy scales. In particular,\nwe show that, in this case, the REM conjecture holds exactly up to energies\n$E_N<\\b_c N$, where $\\b_c$ is the critical temperature. We also explain the\nmore complex behaviour that sets in at higher energies.", "category": "cond-mat_dis-nn" }, { "text": "Two Interacting Electrons in a Quasiperiodic Chain: We study numerically the effect of on-site Hubbard interaction U between two\nelectrons in the quasiperiodic Harper's equation. In the periodic chain limit\nby mapping the problem to that of one electron in two dimensions with a\ndiagonal line of impurities of strength U we demonstrate a band of resonance\ntwo particle pairing states starting from E=U. In the ballistic (metallic)\nregime we show explicitly interaction-assisted extended pairing states and\nmultifractal pairing states in the diffusive (critical) regime. We also obtain\nlocalized pairing states in the gaps and the created subband due to U, whose\nnumber increases when going to the localized regime, which are responsible for\nreducing the velocity and the diffusion coefficient in the qualitatively\nsimilar to the non-interacting case ballistic and diffusive dynamics. In the\nlocalized regime we find propagation enhancement for small U and stronger\nlocalization for larger U, as in disordered systems.", "category": "cond-mat_dis-nn" }, { "text": "Significance of the Hyperfine Interactions in the Phase Diagram of ${\\rm\n LiHo_xY_{1-x}F_4}$: We consider the quantum magnet $\\rm LiHo_xY_{1-x}F_4$ at $x = 0.167$.\nExperimentally the spin glass to paramagnet transition in this system was\nstudied as a function of the transverse magnetic field and temperature, showing\npeculiar features: for example (i) the spin glass order is destroyed much\nfaster by thermal fluctuations than by the transverse field; and (ii) the cusp\nin the nonlinear susceptibility signaling the glass state {\\it decreases} in\nsize at lower temperature. Here we show that the hyperfine interactions of the\nHo atom must dominate in this system, and that along with the transverse\ninter-Ho dipolar interactions they dictate the structure of the phase diagram.\nThe experimental observations are shown to be natural consequences of this.", "category": "cond-mat_dis-nn" }, { "text": "Resilience to damage of graphs with degree correlations: The existence or not of a percolation threshold on power law correlated\ngraphs is a fundamental question for which a general criterion is lacking. In\nthis work we investigate the problems of site and bond percolation on graphs\nwith degree correlations and their connection with spreading phenomena. We\nobtain some general expressions that allow the computation of the transition\nthresholds or their bounds. Using these results we study the effects of\nassortative and disassortative correlations on the resilience to damage of\nnetworks.", "category": "cond-mat_dis-nn" }, { "text": "Effect of second-rank random anisotropy on critical phenomena of random\n field O(N) spin model in the large N limit: We study the critical behavior of a random field O($N$) spin model with a\nsecond-rank random anisotropy term in spatial dimensions $4 Tf = T, which must be accommodated within the landscape\nparadigm. We note that, in appropriate systems, an increase in concentration of\nslow chemically ordering units in liquids can produce a crossover to fast ion\nconducting glass phenomenology.", "category": "cond-mat_dis-nn" }, { "text": "Molecular dynamics computer simulation of amorphous silica under high\n pressure: The structural and dynamic properties of silica melts under high pressure are\nstudied using molecular dynamics (MD) computer simulation. The interactions\nbetween the ions are modeled by a pairwise-additive potential, the so-called\nCHIK potential, that has been recently proposed by Carre et al. The\nexperimental equation of state is well-reproduced by the CHIK model. With\nincreasing pressure (density), the structure changes from a tetrahedral network\nto a network containing a high number of five- and six-fold Si-O coordination.\nIn the partial static structure factors, this change of the structure with\nincreasing density is reflected by a shift of the first sharp diffraction peak\ntowards higher wavenumbers q, eventually merging with the main peak at\ndensities around 4.2 g/cm^3. The self-diffusion constants as a function of\npressure show the experimentally-known maximum, occurring around a pressure of\nabout 20 GPa.", "category": "cond-mat_dis-nn" }, { "text": "Renormalization Group Approach to Spin Glass Systems: A renormalization group transformation suitable for spin glass models and,\nmore generally, for disordered models, is presented. The procedure is\nnon-standard in both the nature of the additional interactions and the coarse\ngraining transformation, that is performed on the overlap probability measure\n(which is clearly non-Gibbsian). Universality classes are thus naturally\ndefined on a large set of models, going from $\\Z_2$ and Gaussian spin glasses\nto Ising and fully frustrated models, and others.", "category": "cond-mat_dis-nn" }, { "text": "Mobility edge and intermediate phase in one-dimensional incommensurate\n lattice potentials: We study theoretically the localization properties of two distinct\none-dimensional quasiperiodic lattice models with a single-particle mobility\nedge (SPME) separating extended and localized states in the energy spectrum.\nThe first one is the familiar Soukoulis-Economou trichromatic potential model\nwith two incommensurate potentials, and the second is a system consisting of\ntwo coupled 1D Aubry-Andre chains each containing one incommensurate potential.\nWe show that as a function of the Hamiltonian model parameters, both models\nhave a wide single-particle intermediate phase (SPIP), defined as the regime\nwhere localized and extended single-particle states coexist in the spectrum,\nleading to a behavior intermediate between purely extended or purely localized\nwhen the system is dynamically quenched from a generic initial state. Our\nresults thus suggest that both systems could serve as interesting experimental\nplatforms for studying the interplay between localized and extended states, and\nmay provide insight into the role of the coupling of small baths to localized\nsystems. We also calculate the Lyapunov (or localization) exponent for several\nincommensurate 1D models exhibiting SPME, finding that such localization\ncritical exponents for quasiperiodic potential induced localization are\nnonuniversal and depend on the microscopic details of the Hamiltonian.", "category": "cond-mat_dis-nn" }, { "text": "Odor recognition and segmentation by a model olfactory bulb and cortex: We present a model of an olfactory system that performs odor segmentation.\nBased on the anatomy and physiology of natural olfactory systems, it consists\nof a pair of coupled modules, bulb and cortex. The bulb encodes the odor inputs\nas oscillating patterns. The cortex functions as an associative memory: When\nthe input from the bulb matches a pattern stored in the connections between its\nunits, the cortical units resonate in an oscillatory pattern characteristic of\nthat odor. Further circuitry transforms this oscillatory signal to a\nslowly-varying feedback to the bulb. This feedback implements olfactory\nsegmentation by suppressing the bulbar response to the pre-existing odor,\nthereby allowing subsequent odors to be singled out for recognition.", "category": "cond-mat_dis-nn" }, { "text": "k-Core percolation on multiplex networks: We generalize the theory of k-core percolation on complex networks to k-core\npercolation on multiplex networks, where k=(k_a, k_b, ...). Multiplex networks\ncan be defined as networks with a set of vertices but different types of edges,\na, b, ..., representing different types of interactions. For such networks, the\nk-core is defined as the largest sub-graph in which each vertex has at least\nk_i edges of each type, i = a, b, ... . We derive self-consistency equations to\nobtain the birth points of the k-cores and their relative sizes for\nuncorrelated multiplex networks with an arbitrary degree distribution. To\nclarify our general results, we consider in detail multiplex networks with\nedges of two types, a and b, and solve the equations in the particular case of\nER and scale-free multiplex networks. We find hybrid phase transitions at the\nemergence points of k-cores except the (1,1)-core for which the transition is\ncontinuous. We apply the k-core decomposition algorithm to air-transportation\nmultiplex networks, composed of two layers, and obtain the size of (k_a,\nk_b)-cores.", "category": "cond-mat_dis-nn" }, { "text": "Comment on \"Collective dynamics in liquid lithium, sodium, and aluminum\": In a recent paper, S. Singh and K. Tankeshwar (ST), [Phys. Rev. E\n\\textbf{67}, 012201 (2003)], proposed a new interpretation of the collective\ndynamics in liquid metals, and, in particular, of the relaxation mechanisms\nruling the density fluctuations propagation. At variance with both the\npredictions of the current literature and the results of recent Inelastic X-ray\nScattering (IXS) experiments, ST associate the quasielastic component of the\n$S(Q,\\omega)$ to the thermal relaxation, as it holds in an ordinary adiabatic\nhydrodynamics valid for non-conductive liquids and in the $Q \\to 0$ limit. We\nshow here that this interpretation leads to a non-physical behaviour of\ndifferent thermodynamic and transport parameters.", "category": "cond-mat_dis-nn" }, { "text": "Breakdown of Dynamical Scale Invariance in the Coarsening of Fractal\n Clusters: We extend a previous analysis [PRL {\\bf 80}, 4693 (1998)] of breakdown of\ndynamical scale invariance in the coarsening of two-dimensional DLAs\n(diffusion-limited aggregates) as described by the Cahn-Hilliard equation.\nExistence of a second dynamical length scale, predicted earlier, is\nestablished. Having measured the \"solute mass\" outside the cluster versus time,\nwe obtain a third dynamical exponent. An auxiliary problem of the dynamics of a\nslender bar (that acquires a dumbbell shape) is considered. A simple scenario\nof coarsening of fractal clusters with branching structure is suggested that\nemploys the dumbbell dynamics results. This scenario involves two dynamical\nlength scales: the characteristic width and length of the cluster branches. The\npredicted dynamical exponents depend on the (presumably invariant) fractal\ndimension of the cluster skeleton. In addition, a robust theoretical estimate\nfor the third dynamical exponent is obtained. Exponents found numerically are\nin reasonable agreement with these predictions.", "category": "cond-mat_dis-nn" }, { "text": "Exact new mobility edges between critical and localized states: The disorder systems host three types of fundamental quantum states, known as\nthe extended, localized, and critical states, of which the critical states\nremain being much less explored. Here we propose a class of exactly solvable\nmodels which host a novel type of exact mobility edges (MEs) separating\nlocalized states from robust critical states, and propose experimental\nrealization. Here the robustness refers to the stability against both\nsingle-particle perturbation and interactions in the few-body regime. The\nexactly solvable one-dimensional models are featured by quasiperiodic mosaic\ntype of both hopping terms and on-site potentials. The analytic results enable\nus to unambiguously obtain the critical states which otherwise require arduous\nnumerical verification including the careful finite size scalings. The critical\nstates and new MEs are shown to be robust, illustrating a generic mechanism\nunveiled here that the critical states are protected by zeros of quasiperiodic\nhopping terms in the thermodynamic limit. Further, we propose a novel\nexperimental scheme to realize the exactly solvable model and the new MEs in an\nincommensurate Rydberg Raman superarray. This work may pave a way to precisely\nexplore the critical states and new ME physics with experimental feasibility.", "category": "cond-mat_dis-nn" }, { "text": "Critical exponents in Ising spin glasses: We determine accurate values of ordering temperatures and critical exponents\nfor Ising Spin Glass transitions in dimension 4, using a combination of finite\nsize scaling and non-equilibrium scaling techniques. We find that the exponents\n$\\eta$ and $z$ vary with the form of the interaction distribution, indicating\nnon-universality at Ising spin glass transitions. These results confirm\nconclusions drawn from numerical data for dimension 3.", "category": "cond-mat_dis-nn" }, { "text": "On the fragility of the mean-field scenario of structural glasses for\n finite-dimensional disordered spin models: At the mean-field level, on fully connected lattices, several disordered spin\nmodels have been shown to belong to the universality class of \"structural\nglasses\", with a \"random first-order transition\" (RFOT) characterized by a\ndiscontinuous jump of the order parameter and no latent heat. However, their\nbehavior in finite dimensions is often drastically different, displaying either\nno glassiness at all or a conventional spin-glass transition. We clarify the\nphysical reasons for this phenomenon and stress the unusual fragility of the\nRFOT to short-range fluctuations, associated e.g. with the mere existence of a\nfinite number of neighbors. Accordingly, the solution of fully connected models\nis only predictive in very high dimension whereas, despite being also\nmean-field in character, the Bethe approximation provides valuable information\non the behavior of finite-dimensional systems. We suggest that before embarking\non a full-blown account of fluctuations on all scales through computer\nsimulation or renormalization-group approach, models for structural glasses\nshould first be tested for the effect of short-range fluctuations and we\ndiscuss ways to do it. Our results indicate that disordered spin models do not\nappear to pass the test and are therefore questionable models for investigating\nthe glass transition in three dimensions. This also highlights how nontrivial\nis the first step of deriving an effective theory for the RFOT phenomenology\nfrom a rigorous integration over the short-range fluctuations.", "category": "cond-mat_dis-nn" }, { "text": "Circumventing spin glass traps by microcanonical spontaneous symmetry\n breaking: The planted p-spin interaction model is a paradigm of random-graph systems\npossessing both a ferromagnetic phase and a disordered phase with the latter\nsplitting into many spin glass states at low temperatures. Conventional\nsimulated annealing dynamics is easily blocked by these low-energy spin glass\nstates. Here we demonstrate that, actually this planted system is exponentially\ndominated by a microcanonical polarized phase at intermediate energy densities.\nThere is a discontinuous microcanonical spontaneous symmetry breaking\ntransition from the paramagnetic phase to the microcanonical polarized phase.\nThis transition can serve as a mechanism to avoid all the spin glass traps, and\nit is accelerated by the restart strategy of microcanonical random walk. We\nalso propose an unsupervised learning problem on microcanonically sampled\nconfigurations for inferring the planted ground state.", "category": "cond-mat_dis-nn" }, { "text": "Dynamics of fractal dimension during phase ordering of a geometrical\n multifractal: A simple multifractal coarsening model is suggested that can explain the\nobserved dynamical behavior of the fractal dimension in a wide range of\ncoarsening fractal systems. It is assumed that the minority phase (an ensemble\nof droplets) at $t=0$ represents a non-uniform recursive fractal set, and that\nthis set is a geometrical multifractal characterized by a $f(\\alpha)$-curve. It\nis assumed that the droplets shrink according to their size and preserving\ntheir ordering. It is shown that at early times the Hausdorff dimension does\nnot change with time, whereas at late times its dynamics follow the $f(\\alpha)$\ncurve. This is illustrated by a special case of a two-scale Cantor dust. The\nresults are then generalized to a wider range of coarsening mechanisms.", "category": "cond-mat_dis-nn" }, { "text": "Atomic structure of the continuous random network of amorphous\n C[(C6H4)2]2, PAF-1: We demonstrate that the amorphous material PAF-1, C[(C6H4)2]2, forms a\ncontinuous random network in which tetrahedral carbon sites are connected by\n4,4'-biphenyl linkers. Experimental neutron total scattering measurements on\ndeuterated, hydrogenous, and null-scattering samples agree with molecular\ndynamics simulations based on this model. From the MD model, we are able for\nthe first time to interrogate the atomistic structure. The small-angle\nscattering is consistent with Porod scattering from particle surfaces, of the\nform Q^{-4}, where Q is the scattering vector. We measure a distinct peak in\nthe scattering at Q = 0.45 {\\AA}^{-1}, corresponding to the first sharp\ndiffraction peak in amorphous silica, which indicates the structural analogy\nbetween these two amorphous tetrahedral networks.", "category": "cond-mat_dis-nn" }, { "text": "Finite size effects in the microscopic critical properties of jammed\n configurations: A comprehensive study of the effects of different types of\n disorder: Jamming criticality defines a universality class that includes systems as\ndiverse as glasses, colloids, foams, amorphous solids, constraint satisfaction\nproblems, neural networks, etc. A particularly interesting feature of this\nclass is that small interparticle forces ($f$) and gaps ($h$) are distributed\naccording to nontrivial power laws. A recently developed mean-field (MF) theory\npredicts the characteristic exponents of these distributions in the limit of\nvery high spatial dimension, $d\\rightarrow\\infty$ and, remarkably, their values\nseemingly agree with numerical estimates in physically relevant dimensions,\n$d=2$ and $3$. These exponents are further connected through a pair of\ninequalities derived from stability conditions, and both theoretical\npredictions and previous numerical investigations suggest that these\ninequalities are saturated. Systems at the jamming point are thus only\nmarginally stable. Despite the key physical role played by these exponents,\ntheir systematic evaluation has yet to be attempted. Here, we carefully test\ntheir value by analyzing the finite-size scaling of the distributions of $f$\nand $h$ for various particle-based models for jamming. Both dimension and the\ndirection of approach to the jamming point are also considered. We show that,\nin all models, finite-size effects are much more pronounced in the distribution\nof $h$ than in that of $f$. We thus conclude that gaps are correlated over\nconsiderably longer scales than forces. Additionally, remarkable agreement with\nMF predictions is obtained in all but one model, namely near-crystalline\npackings. Our results thus help to better delineate the domain of the jamming\nuniversality class. We furthermore uncover a secondary linear regime in the\ndistribution tails of both $f$ and $h$. This surprisingly robust feature is\nunderstood to follow from the (near) isostaticity of our configurations.", "category": "cond-mat_dis-nn" }, { "text": "Rayleigh anomalies and disorder-induced mixing of polarizations at\n nanoscale in amorphous solids. Testing 1-octyl-3-methylimidazolium chloride\n glass: Acoustic excitations in topologically disordered media at mesoscale present\nanomalous features with respect to the Debye's theory. In a three-dimensional\nmedium an acoustic excitation is characterized by its phase velocity, intensity\nand polarization. The so-called Rayleigh anomalies, which manifest in\nattenuation and retardation of the acoustic excitations, affect the first two\nproperties. The topological disorder is, however, expected to influence also\nthe third one. Acoustic excitations with a well-defined polarization in the\ncontinuum limit present indeed a so-called mixing of polarizations at\nnanoscale, as attested by experimental observations and Molecular Dynamics\nsimulations. We provide a comprehensive experimental characterization of\nacoustic dynamics properties of a selected glass, 1-octyl-3-methylimidazolium\nchloride glass, whose heterogeneous structure at nanoscale is well-assessed.\nDistinctive features, which can be related to the occurrence of the Rayleigh\nanomalies and of the mixing of polarizations are observed. We develop, in the\nframework of the Random Media Theory, an analytical model that allows a\nquantitative description of all the Rayleigh anomalies and the mixing of\npolarizations. Contrast between theoretical and experimental features for the\nselected glass reveals an excellent agreement. The quantitative theoretical\napproach permits thus to demonstrate how the mixing of polarizations generates\ndistinctive feature in the dynamic structure factor of glasses and to\nunambiguously identify them. The robustness of the proposed theoretical\napproach is validated by its ability to describe as well transverse acoustic\ndynamics.", "category": "cond-mat_dis-nn" }, { "text": "Mott, Floquet, and the response of periodically driven Anderson\n insulators: We consider periodically driven Anderson insulators. The short time behavior\nfor weak, monochromatic, uniform electric fields is given by linear response\ntheory and was famously derived by Mott. We go beyond this to consider both\nlong times---which is the physics of Floquet late time states---and strong\nelectric fields. This results in a `phase diagram' in the frequency-field\nstrength plane, in which we identify four distinct regimes. These are: a linear\nresponse regime dominated by pre-existing Mott resonances, which exists\nprovided Floquet saturation is not reached within a period; a non-linear\nperturbative regime, which exhibits multiphoton-absorption in response to the\nfield; a near-adiabatic regime, which exhibits a primarily reactive response\nspread over the entire sample and is insensitive to pre-existing resonances;\nand finally an enhanced dissipative regime.", "category": "cond-mat_dis-nn" }, { "text": "Phase Transition in a Random Minima Model: Mean Field Theory and Exact\n Solution on the Bethe Lattice: We consider the number and distribution of minima in random landscapes\ndefined on non-Euclidean lattices. Using an ensemble where random landscapes\nare reweighted by a fugacity factor $z$ for each minimum they contain, we\nconstruct first a `two-box' mean field theory. This exhibits an ordering phase\ntransition at $z\\c=2$ above which one box contains an extensive number of\nminima. The onset of order is governed by an unusual order parameter exponent\n$\\beta=1$, motivating us to study the same model on the Bethe lattice. Here we\nfind from an exact solution that for any connectivity $\\mu+1>2$ there is an\nordering transition with a conventional mean field order parameter exponent\n$\\beta=1/2$, but with the region where this behaviour is observable shrinking\nin size as $1/\\mu$ in the mean field limit of large $\\mu$. We show that the\nbehaviour in the transition region can also be understood directly within a\nmean field approach, by making the assignment of minima `soft'. Finally we\ndemonstrate, in the simplest mean field case, how the analysis can be\ngeneralized to include both maxima and minima. In this case an additional first\norder phase transition appears, to a landscape in which essentially all sites\nare either minima or maxima.", "category": "cond-mat_dis-nn" }, { "text": "Logarithmically Slow Relaxation in Quasi-Periodically Driven Random Spin\n Chains: We simulate the dynamics of a disordered interacting spin chain subject to a\nquasi-periodic time-dependent drive, corresponding to a stroboscopic Fibonacci\nsequence of two distinct Hamiltonians. Exploiting the recursive drive\nstructure, we can efficiently simulate exponentially long times. After an\ninitial transient, the system exhibits a long-lived glassy regime characterized\nby a logarithmically slow growth of entanglement and decay of correlations\nanalogous to the dynamics at the many-body delocalization transition.\nUltimately, at long time-scales, which diverge exponentially for weak or rapid\ndrives, the system thermalizes to infinite temperature. The slow relaxation\nenables metastable dynamical phases, exemplified by a \"time quasi-crystal\" in\nwhich spins exhibit persistent oscillations with a distinct quasi-periodic\npattern from that of the drive. We show that in contrast with Floquet systems,\na high-frequency expansion strictly breaks down above fourth order, and fails\nto produce an effective static Hamiltonian that would capture the pre-thermal\nglassy relaxation.", "category": "cond-mat_dis-nn" }, { "text": "Comment on \"Explicit Analytical Solution for Random Close Packing in d=2\n and d=3\", Physical Review Letters {\\bf 128}, 028002 (2022): The method, proposed in \\cite{Za22} to derive the densest packing fraction of\nrandom disc and sphere packings, is shown to yield in two dimensions too high a\nvalue that (i) violates the very assumption underlying the method and (ii)\ncorresponds to a high degree of structural order. The claim that the obtained\nvalue is supported by a specific simulation is shown to be unfounded. One\nsource of the error is pointed out.", "category": "cond-mat_dis-nn" }, { "text": "Fluctuations in photon local delay time and their relation to phase\n spectra in random media: The temporal evolution of microwave pulses transmitted through random\ndielectric samples is obtained from the Fourier transform of field spectra.\nLarge fluctuations are found in the local or single channel delay time, which\nis the first temporal moment of the transmitted pulse at a point in the output\nspeckle pattern. Both positive and negative values of local delay time are\nobserved. The widest distribution is found at low intensity values near a phase\nsingularity in the transmitted speckle pattern. In the limit of long duration,\nnarrow-bandwidth incident pulses, the single channel delay time equals the\nspectral derivative of the phase of the transmitted field. Fluctuations of the\nphase of the transmitted field thus reflect the underlying statistics of\ndynamics in mesoscopic systems.", "category": "cond-mat_dis-nn" }, { "text": "Order Parameter Criticality of the d=3 Random-Field Ising\n Antiferromagnet Fe(0.85)Zn(0.15)F2: The critical exponent beta =0.16 +- 0.02 for the random-field Ising model\norder parameter is determined using extinction-free magnetic x-ray scattering\nfor Fe(0.85)Zn(0.15)F2 in magnetic fields of 10 and 11 T. The observed value is\nconsistent with other experimental random-field critical exponents, but\ndisagrees sharply with Monte Carlo and exact ground state calculations on\nfinite-sized systems.", "category": "cond-mat_dis-nn" }, { "text": "Non-perturbative results for level correlations from the replica\n nonlinear sigma model: We show that for all the three standard symmetry classes (unitary, orthogonal\nand symplectic), the conventional replica nonlinear sigma model gives the\ncorrect non-perturbative result for the two-level correlation functions\nR_2(\\omega) of electrons in disordered metals in the limit of large \\omega. In\nthis limit, non-perturbative oscillatory contributions arise from a degenerate\nsaddle-point manifold within this sigma model which corresponds to the\nreplica-symmetry breaking. Moreover, we demonstrate that in the unitary case\nthe very same results can be extracted from the well known exact integral\nrepresentation for R_2(\\omega).", "category": "cond-mat_dis-nn" }, { "text": "Phase transitions in the $q$-coloring of random hypergraphs: We study in this paper the structure of solutions in the random hypergraph\ncoloring problem and the phase transitions they undergo when the density of\nconstraints is varied. Hypergraph coloring is a constraint satisfaction problem\nwhere each constraint includes $K$ variables that must be assigned one out of\n$q$ colors in such a way that there are no monochromatic constraints, i.e.\nthere are at least two distinct colors in the set of variables belonging to\nevery constraint. This problem generalizes naturally coloring of random graphs\n($K=2$) and bicoloring of random hypergraphs ($q=2$), both of which were\nextensively studied in past works. The study of random hypergraph coloring\ngives us access to a case where both the size $q$ of the domain of the\nvariables and the arity $K$ of the constraints can be varied at will. Our work\nprovides explicit values and predictions for a number of phase transitions that\nwere discovered in other constraint satisfaction problems but never evaluated\nbefore in hypergraph coloring. Among other cases we revisit the hypergraph\nbicoloring problem ($q=2$) where we find that for $K=3$ and $K=4$ the\ncolorability threshold is not given by the one-step-replica-symmetry-breaking\nanalysis as the latter is unstable towards more levels of replica symmetry\nbreaking. We also unveil and discuss the coexistence of two different 1RSB\nsolutions in the case of $q=2$, $K \\ge 4$. Finally we present asymptotic\nexpansions for the density of constraints at which various phase transitions\noccur, in the limit where $q$ and/or $K$ diverge.", "category": "cond-mat_dis-nn" }, { "text": "Dynamic mean-field and cavity methods for diluted Ising systems: We compare dynamic mean-field and dynamic cavity as methods to describe the\nstationary states of dilute kinetic Ising models. We compute dynamic mean-field\ntheory by expanding in interaction strength to third order, and compare to the\nexact dynamic mean-field theory for fully asymmetric networks. We show that in\ndiluted networks the dynamic cavity method generally predicts magnetizations of\nindividual spins better than both first order (\"naive\") and second order\n(\"TAP\") dynamic mean field theory.", "category": "cond-mat_dis-nn" }, { "text": "Breakdown of self-averaging in the Bose glass: We study the square-lattice Bose-Hubbard model with bounded random on-site\nenergies at zero temperature. Starting from a dual representation obtained from\na strong-coupling expansion around the atomic limit, we employ a real-space\nblock decimation scheme. This approach is non-perturbative in the disorder and\nenables us to study the renormalization-group flow of the induced random-mass\ndistribution. In both insulating phases, the Mott insulator and the Bose glass,\nthe average mass diverges, signaling short range superfluid correlations. The\nrelative variance of the mass distribution distinguishes the two phases,\nrenormalizing to zero in the Mott insulator and diverging in the Bose glass.\nNegative mass values in the tail of the distribution indicate the presence of\nrare superfluid regions in the Bose glass. The breakdown of self-averaging is\nevidenced by the divergent relative variance and increasingly non-Gaussian\ndistributions. We determine an explicit phase boundary between the Mott\ninsulator and Bose glass.", "category": "cond-mat_dis-nn" }, { "text": "Dynamics of quantum information in many-body localized systems: We characterize the information dynamics of strongly disordered systems using\na combination of analytics, exact diagonalization, and matrix product operator\nsimulations. More specifically, we study the spreading of quantum information\nin three different scenarios: thermalizing, Anderson localized, and many-body\nlocalized. We qualitatively distinguish these cases by quantifying the amount\nof remnant information in a local region. The nature of the dynamics is further\nexplored by computing the propagation of mutual information with respect to\nvarying partitions. Finally, we demonstrate that classical simulability, as\ncaptured by the magnitude of MPO truncation errors, exhibits enhanced\nfluctuations near the localization transition, suggesting the possibility of\nits use as a diagnostic of the critical point.", "category": "cond-mat_dis-nn" }, { "text": "Comment on \"Collective dynamics in liquid lithium, sodium, and aluminum\": In a recent paper, S. Singh and K. Tankeshwar (ST), [Phys. Rev. E\n\\textbf{67}, 012201 (2003)], proposed a new interpretation of the collective\ndynamics in liquid metals, and, in particular, of the relaxation mechanisms\nruling the density fluctuations propagation. At variance with both the\npredictions of the current literature and the results of recent Inelastic X-ray\nScattering (IXS) experiments, ST associate the quasielastic component of the\n$S(Q,\\omega)$ to the thermal relaxation, as it holds in an ordinary adiabatic\nhydrodynamics valid for non-conductive liquids and in the $Q \\to 0$ limit. We\nshow here that this interpretation leads to a non-physical behaviour of\ndifferent thermodynamic and transport parameters.", "category": "cond-mat_dis-nn" }, { "text": "Many-body localization as a large family of localized ground states: Many-body localization (MBL) addresses the absence of thermalization in\ninteracting quantum systems, with non-ergodic high-energy eigenstates behaving\nas ground states, only area-law entangled. However, computing highly excited\nmany-body eigenstates using exact methods is very challenging. Instead, we show\nthat one can address high-energy MBL physics using ground-state methods, which\nare much more amenable to many efficient algorithms. We find that a localized\nmany-body ground state of a given interacting disordered Hamiltonian\n$\\mathcal{H}_0$ is a very good approximation for a high-energy eigenstate of a\nparent Hamiltonian, close to $\\mathcal{H}_0$ but more disordered. This\nconstruction relies on computing the covariance matrix, easily achieved using\ndensity-matrix renormalization group for disordered Heisenberg chains up to\n$L=256$ sites.", "category": "cond-mat_dis-nn" }, { "text": "Exact results and new insights for models defined over small-world\n networks. First and second order phase transitions. I: General result: We present, as a very general method, an effective field theory to analyze\nmodels defined over small-world networks. Even if the exactness of the method\nis limited to the paramagnetic regions and to some special limits, it gives the\nexact critical behavior and the exact critical surfaces and percolation\nthresholds, and provide a clear and immediate (also in terms of calculation)\ninsight of the physics. The underlying structure of the non random part of the\nmodel, i.e., the set of spins staying in a given lattice L_0 of dimension d_0\nand interacting through a fixed coupling J_0, is exactly taken into account.\nWhen J_0\\geq 0, the small-world effect gives rise to the known fact that a\nsecond order phase transition takes place, independently of the dimension d_0\nand of the added random connectivity c. However, when J_0<0, a completely\ndifferent scenario emerges where, besides a spin glass transition, multiple\nfirst- and second-order phase transitions may take place.", "category": "cond-mat_dis-nn" }, { "text": "Lack of Evidence for a Singlet Crystal Field Ground State in the\n Tb2Ti2O7 Magnetic Pyrochlore: We present new high resolution inelastic neutron scattering data on the\ncandidate spin liquid Tb2Ti2O7. We find that there is no evidence for a zero\nfield splitting of the ground state doublet within the 0.2 K resolution of the\ninstrument. This result contrasts with a pair of recent works on Tb2Ti2O7\nclaiming that the spin liquid behavior can be attributed to a 2 K split\nsinglet-singlet single-ion spectrum at low energies. We also reconsider the\nentropy argument presented in Chapuis {\\it et al.} as further evidence of a\nsinglet-singlet crystal field spectrum. We arrive at the conclusion that\nestimates of the low temperature residual entropy drawn from heat capacity\nmeasurements are a poor guide to the single ion spectrum without understanding\nthe nature of the correlations.", "category": "cond-mat_dis-nn" }, { "text": "Jamming and replica symmetry breaking of weakly disordered crystals: We discuss the physics of crystals with small polydispersity near the jamming\ntransition point. For this purpose, we introduce an effective single-particle\nmodel taking into account the nearest neighbor structure of crystals. The model\ncan be solved analytically by using the replica method in the limit of large\ndimensions. In the absence of polydispersity, the replica symmetric solution is\nstable until the jamming transition point, which leads to the standard scaling\nof perfect crystals. On the contrary, for finite polydispersity, the model\nundergoes the full replica symmetry breaking (RSB) transition before the\njamming transition point. In the RSB phase, the model exhibits the same scaling\nas amorphous solids near the jamming transition point. These results are fully\nconsistent with the recent numerical simulations of crystals with\npolydispersity. The simplicity of the model also allows us to derive the\nscaling behavior of the vibrational density of states that can be tested in\nfuture experiments and numerical simulations.", "category": "cond-mat_dis-nn" }, { "text": "Universal scaling of distances in complex networks: Universal scaling of distances between vertices of Erdos-Renyi random graphs,\nscale-free Barabasi-Albert models, science collaboration networks, biological\nnetworks, Internet Autonomous Systems and public transport networks are\nobserved. A mean distance between two nodes of degrees k_i and k_j equals to\n=A-B log(k_i k_j). The scaling is valid over several decades. A simple\ntheory for the appearance of this scaling is presented. Parameters A and B\ndepend on the mean value of a node degree _nn calculated for the nearest\nneighbors and on network clustering coefficients.", "category": "cond-mat_dis-nn" }, { "text": "Application of a multi-site mean-field theory to the disordered\n Bose-Hubbard model: We present a multi-site formulation of mean-field theory applied to the\ndisordered Bose-Hubbard model. In this approach the lattice is partitioned into\nclusters, each isolated cluster being treated exactly, with inter-cluster\nhopping being treated approximately. The theory allows for the possibility of a\ndifferent superfluid order parameter at every site in the lattice, such as what\nhas been used in previously published site-decoupled mean-field theories, but a\nmulti-site formulation also allows for the inclusion of spatial correlations\nallowing us, e.g., to calculate the correlation length (over the length scale\nof each cluster). We present our numerical results for a two-dimensional\nsystem. This theory is shown to produce a phase diagram in which the stability\nof the Mott insulator phase is larger than that predicted by site-decoupled\nsingle-site mean-field theory. Two different methods are given for the\nidentification of the Bose glass-to-superfluid transition, one an approximation\nbased on the behaviour of the condensate fraction, and one of which relies on\nobtaining the spatial variation of the order parameter correlation. The\nrelation of our results to a recent proposal that both transitions are non\nself-averaging is discussed.", "category": "cond-mat_dis-nn" }, { "text": "Millisecond Electron-Phonon Relaxation in Ultrathin Disordered Metal\n Films at Millikelvin Temperatures: We have measured directly the thermal conductance between electrons and\nphonons in ultra-thin Hf and Ti films at millikelvin temperatures. The\nexperimental data indicate that electron-phonon coupling in these films is\nsignificantly suppressed by disorder. The electron cooling time $\\tau_\\epsilon$\nfollows the $T^{-4}$-dependence with a record-long value $\\tau_\\epsilon=25ms$\nat $T=0.04K$. The hot-electron detectors of far-infrared radiation, fabricated\nfrom such films, are expected to have a very high sensitivity. The noise\nequivalent power of a detector with the area $1\\mum^2$ would be\n$(2-3)10^{-20}W/Hz^{1/2}$, which is two orders of magnitude smaller than that\nof the state-of-the-art bolometers.", "category": "cond-mat_dis-nn" }, { "text": "Relation of the thermodynamic parameter of disordering with the width of\n structure factor and defect concentration in a metallic glass: In this work, we show that above the glass transition there exists a strong\nunique interrelationship between the thermodynamic parameter of disorder of a\nmetallic glass derived using its excess entropy, diffraction measure of\ndisorder given by the width of the X-ray structure factor and defect\nconcentration derived from shear modulus measurements. Below the glass\ntransition, this relationship is more complicated and depends on both\ntemperature and thermal prehistory.", "category": "cond-mat_dis-nn" }, { "text": "A method of effective potentials for calculating the frequency spectrum\n of eccentrically layered spherical cavity resonators: A novel method for the calculation of eigenfrequencies of non-uniformly\nfilled spherical cavity resonators is developed. The impact of the system\nsymmetry on the electromagnetic field distribution as well as on its degrees of\nfreedom (the set of resonant modes) is examined. It is shown that in the case\nof angularly symmetric cavity, regardless of its radial non-uniformity, the set\nof resonator modes is, as anticipated, a superposition of TE and TM\noscillations which can be described in terms of a single scalar function\nindependently of each other. The spectrum is basically determined through the\nintroduction of effective ``dynamic'' potentials which encode the infill\ninhomogeneity. The violation of polar symmetry in the infill dielectric\nproperties, the azimuthal symmetry being simultaneously preserved, suppresses\nall azimuthally non-uniform modes of electric-type (TM) oscillations. In the\nabsence of angular symmetry of both electric and magnetic properties of the\nresonator infill, only azimuthally uniform distribution of both TM and TE\nfields is expected to occur in the resonator. The comparison is made of the\nresults obtained through the proposed method and of the test problem solution\nobtained with use of commercial solvers. The method appears to be efficient for\ncomputational complex algorithms for solving spectral problems, including those\nfor studying the chaotic properties of electrodynamic systems' spectra.", "category": "cond-mat_dis-nn" }, { "text": "Long-range influence of manipulating disordered-insulators locally: Localization of wavefunctions is arguably the most familiar effect of\ndisorder in quantum systems. It has been recently argued [[V. Khemani, R.\nNandkishore, and S. L. Sondhi, Nature Physics, 11, 560 (2015)] that, contrary\nto naive expectation, manipulation of a localized-site in the disordered medium\nmay produce a disturbance over a length-scale much larger than the\nlocalization-length $\\xi$. Here we report on the observation of this nonlocal\nphenomenon in electronic transport experiment. Being a wave property,\nvisibility of this effect hinges upon quantum-coherence, and its spatial-scale\nmay be ultimately limited by the phase-coherent length of the disordered\ninsulator. Evidence for quantum coherence in the Anderson-insulating phase may\nbe obtained from magneto-resistance measurements which however are useful\nmainly in thin-films. The technique used in this work offers an empirical\nmethod to measure this fundamental aspect of Anderson-insulators even in\nrelatively thick samples.", "category": "cond-mat_dis-nn" }, { "text": "On the shape of invading population in oriented environments: We analyze the properties of population spreading in environments with\nspatial anisotropy within the frames of a lattice model of asymmetric (biased)\nrandom walkers. The expressions for the universal shape characteristics of the\ninstantaneous configuration of population, such as asphericity $A$ and\nprolateness $S$ are found analytically and proved to be dependent only on the\nasymmetric transition probabilities in different directions. The model under\nconsideration is shown to capture, in particular, the peculiarities of invasion\nin presence of an array of oriented tubes (fibers) in the environment.", "category": "cond-mat_dis-nn" }, { "text": "Carrier induced ferromagnetism in diluted local-moment systems: The electronic and magnetic properties of concentrated and diluted\nferromagnetic semiconductors are investigated by using the Kondo lattice model,\nwhich describes an interband exchange coupling between itinerant conduction\nelectrons and localized magnetic moments. In our calculations, the electronic\nproblem and the local magnetic problem are solved separately. For the\nelectronic part an interpolating self-energy approach together with a coherent\npotential approximation (CPA) treatment of a dynamical alloy analogy is used to\ncalculate temperature-dependent quasiparticle densities of states and the\nelectronic self-energy of the diluted local-moment system. For constructing the\nmagnetic phase diagram we use a modified RKKY theory by mapping the interband\nexchange to an effective Heisenberg model. The exchange integrals appear as\nfunctionals of the diluted electronic self-energy being therefore temperature-\nand carrier-concentration-dependent and covering RKKY as well as double\nexchange behavior. The disorder of the localized moments in the effective\nHeisenberg model is solved by a generalized locator CPA approach. The main\nresults are: 1) extremely low carrier concentrations are sufficient to induce\nferromagnetism; 2) the Curie temperature exhibits a strikingly non-monotonic\nbehavior as a function of carrier concentration with a distinct maximum; 3)\n$T_C$ curves break down at critical $n/x$ due to antiferromagnetic correlations\nand 4) the dilution always lowers $T_C$ but broadens the ferromagnetic region\nwith respect to carrier concentration.", "category": "cond-mat_dis-nn" }, { "text": "Instability of speckle patterns in random media with noninstantaneous\n Kerr nonlinearity: Onset of the instability of a multiple-scattering speckle pattern in a random\nmedium with Kerr nonlinearity is significantly affected by the noninstantaneous\ncharacter of the nonlinear medium response. The fundamental time scale of the\nspontaneous speckle dynamics beyond the instability threshold is set by the\nlargest of times $T_{\\mathrm{D}}$ and $\\tau_{\\mathrm{NL}}$, where\n$T_{\\mathrm{D}}$ is the time required for the multiple-scattered waves to\npropagate through the random sample and $\\tau_{\\mathrm{NL}}$ is the relaxation\ntime of the nonlinearity. Inertial nature of the nonlinearity should complicate\nthe experimental observation of the instability phenomenon.", "category": "cond-mat_dis-nn" }, { "text": "Comment on \"Evidence for nontrivial ground-state structure of 3d +/- J\n spin glasses\": In a recent Letter [Europhys. Lett. 40, 429 (1997)], Hartmann presented\nresults for the structure of the degenerate ground states of the\nthree-dimensional +/- J spin glass model obtained using a genetic algorithm. In\nthis Comment, I argue that the method does not produce the correct\nthermodynamic distribution of ground states and therefore gives erroneous\nresults for the overlap distribution. I present results of simulated annealing\ncalculations using different annealing rates for cubic lattices with\nN=4*4*4spins. The disorder-averaged overlap distribution exhibits a significant\ndependence on the annealing rate, even when the energy has converged. For fast\nannealing, moments of the distribution are similar to those presented by\nHartmann. However, as the annealing rate is lowered, they approach the results\npreviously obtained using a multi-canonical Monte Carlo method. This shows\nexplicitly that care must be taken not only to reach states with the lowest\nenergy but also to ensure that they obey the correct thermodynamic\ndistribution, i.e., that the probability is the same for reaching any of the\nground states.", "category": "cond-mat_dis-nn" }, { "text": "Phase Transition in Multiprocessor Scheduling: The problem of distributing the workload on a parallel computer to minimize\nthe overall runtime is known as Multiprocessor Scheduling Problem. It is\nNP-hard, but like many other NP-hard problems, the average hardness of random\ninstances displays an ``easy-hard'' phase transition. The transition in\nMultiprocessor Scheduling can be analyzed using elementary notions from\ncrystallography (Bravais lattices) and statistical mechanics (Potts vectors).\nThe analysis reveals the control parameter of the transition and its critical\nvalue including finite size corrections. The transition is identified in the\nperformance of practical scheduling algorithms.", "category": "cond-mat_dis-nn" }, { "text": "Simple models of small world networks with directed links: We investigate the effect of directed short and long range connections in a\nsimple model of small world network. Our model is such that we can determine\nmany quantities of interest by an exact analytical method. We calculate the\nfunction $V(T)$, defined as the number of sites affected up to time $T$ when a\nnaive spreading process starts in the network. As opposed to shortcuts, the\npresence of un-favorable bonds has a negative effect on this quantity. Hence\nthe spreading process may not be able to affect all the network. We define and\ncalculate a quantity named the average size of accessible world in our model.\nThe interplay of shortcuts, and un-favorable bonds on the small world\nproperties is studied.", "category": "cond-mat_dis-nn" }, { "text": "Potts Glass on Random Graphs: We solve the q-state Potts model with anti-ferromagnetic interactions on\nlarge random lattices of finite coordination. Due to the frustration induced by\nthe large loops and to the local tree-like structure of the lattice this model\nbehaves as a mean field spin glass. We use the cavity method to compute the\ntemperature-coordination phase diagram and to determine the location of the\ndynamic and static glass transitions, and of the Gardner instability. We show\nthat for q>=4 the model possesses a phenomenology similar to the one observed\nin structural glasses. We also illustrate the links between the positive and\nthe zero-temperature cavity approaches, and discuss the consequences for the\ncoloring of random graphs. In particular we argue that in the colorable region\nthe one-step replica symmetry breaking solution is stable towards more steps of\nreplica symmetry breaking.", "category": "cond-mat_dis-nn" }, { "text": "Depinning in a two-layer model of plastic flow: We study a model of two layers, each consisting of a d-dimensional elastic\nobject driven over a random substrate, and mutually interacting through a\nviscous coupling. For this model, the mean-field theory (i.e. a fully connected\nmodel) predicts a transition from elastic depinning to hysteretic plastic\ndepinning as disorder or viscous coupling is increased. A functional RG\nanalysis shows that any small inter-layer viscous coupling destablizes the\nstandard (decoupled) elastic depinning FRG fixed point for d <= 4, while for d\n> 4 most aspects of the mean-field theory are recovered. A one-loop study at\nnon-zero velocity indicates, for d<4, coexistence of a moving state and a\npinned state below the elastic depinning threshold, with hysteretic plastic\ndepinning for periodic and non-periodic driven layers. A 2-loop analysis of\nquasi-statics unveils the possibility of more subtle effects, including a new\nuniversality class for non-periodic objects. We also study the model in d=0,\ni.e. two coupled particles, and show that hysteresis does not always exist as\nthe periodic steady state with coupled layers can be dynamically unstable. It\nis also proved that stable pinned configurations remain dynamically stable in\npresence of a viscous coupling in any dimension d. Moreover, the layer model\nfor periodic objects is stable to an infinitesimal commensurate density\ncoupling. Our work shows that a careful study of attractors in phase space and\ntheir basin of attraction is necessary to obtain a firm conclusion for\ndimensions d=1,2,3.", "category": "cond-mat_dis-nn" }, { "text": "Double-Well Optical Lattices with Atomic Vibrations and Mesoscopic\n Disorder: Double-well optical lattice in an insulating state is considered. The\ninfluence of atomic vibrations and mesoscopic disorder on the properties of the\nlattice are studied. Vibrations lead to the renormalization of atomic\ninteractions. The occurrence of mesoscopic disorder results in the appearance\nof first-order phase transitions between the states with different levels of\natomic imbalance. The existence of a nonuniform external potential, such as\ntrapping potential, essentially changes the lattice properties, suppressing the\ndisorder fraction and rising the transition temperature.", "category": "cond-mat_dis-nn" }, { "text": "Noncollinear magnetic order in quasicrystals: Based on Monte-Carlo simulations, the stable magnetization configurations of\nan antiferromagnet on a quasiperiodic tiling are derived theoretically. The\nexchange coupling is assumed to decrease exponentially with the distance\nbetween magnetic moments. It is demonstrated that the superposition of\ngeometric frustration with the quasiperiodic ordering leads to a\nthree-dimensional noncollinear antiferromagnetic spin structure. The structure\ncan be divided into several ordered interpenetrating magnetic supertilings of\ndifferent energy and characteristic wave vector. The number and the symmetry of\nsubtilings depend on the quasiperiodic ordering of atoms.", "category": "cond-mat_dis-nn" }, { "text": "The Random-Diluted Triangular Plaquette Model: study of phase\n transitions in a Kinetically Constrained Model: We study how the thermodynamic properties of the Triangular Plaquette Model\n(TPM) are influenced by the addition of extra interactions. The thermodynamics\nof the original TPM is trivial, while its dynamics is glassy, as usual in\nKinetically Constrained Models. As soon as we generalize the model to include\nadditional interactions, a thermodynamic phase transition appears in the\nsystem. The additional interactions we consider are either short ranged,\nforming a regular lattice in the plane, or long ranged of the small-world kind.\nIn the case of long-range interactions we call the new model Random-Diluted\nTPM. We provide arguments that the model so modified should undergo a\nthermodynamic phase transition, and that in the long-range case this is a glass\ntransition of the \"Random First-Order\" kind. Finally, we give support to our\nconjectures studying the finite temperature phase diagram of the Random-Diluted\nTPM in the Bethe approximation. This corresponds to the exact calculation on\nthe random regular graph, where free-energy and configurational entropy can be\ncomputed by means of the cavity equations.", "category": "cond-mat_dis-nn" }, { "text": "Ideal strength of random alloys from first-principles theory: The all-electron exact muffin-tin orbitals method in combination with the\ncoherent-potential appproximation has been employed to investigate the ideal\ntensile strengths of elemental V, Mo solids and V- and Mo-based random solid\nsolutions. The present ideal tensile strengths, calculated assuming isotropic\nPoisson contraction, are 16.1, 26.7 and 37.6 GPa for bcc V in the [001], [111]\nand [110] directions, respectively, and 26.7 GPa for bcc Mo in the [001]\ndirection, which are all in good agreement with the available theoretical data.\nWhen a few percent Tc is introduced in Mo, it is found that the ideal strength\ndecreases in the [001] direction. For the V-based alloys, Cr increases and Ti\ndecreases the ideal tensile strength in all principal directions. Adding the\nsame concentration of Cr and Ti to V leads to ternary alloys with similar ideal\nstrength values as that of pure V. The alloying effects on the ideal strength\nis explained using the electronic band structure.", "category": "cond-mat_dis-nn" }, { "text": "Aging is - almost - like equilibrium: We study and compare equilibrium and aging dynamics on both sides of the\nideal glass transition temperature $T_{MCT}$. In the context of a mean field\nmodel, we observe that all dynamical behaviors are determined by the energy\ndistance $\\epsilon$ to threshold - i.e. marginally stable - states. We\nfurthermore show the striking result that after eliminating age and temperature\nat the benefit of $\\epsilon$, the scaling behaviors above and below $T_{MCT}$\nare identical, reconciling {\\it en passant} the mean field results with\nexperimental observations. In the vicinity of the transition, we show that\nthere is an exact mapping between equilibrium dynamics and aging dynamics. This\nleads to very natural interpretations and quantitative predictions for several\nremarkable features of aging dynamics: waiting time-temperature superposition,\ninterrupted aging, dynamical heterogeneity.", "category": "cond-mat_dis-nn" }, { "text": "Incorrect sample classification in \"Electron localization induced by\n intrinsic anion disorder in a transition metal oxynitride\": In the recent study of the metal-insulator transition (MIT) in the disordered\ncrystalline solid SrNbO$_{3-x}$N$_x$ by Daichi Oka et al. [Commun. Phys. 4, 269\n(2021)], the data evaluation relies on the Al'tshuler-Aronov theory of the\ninterference of electron-electron interaction and elastic impurity scattering\nof electrons. The present comment shows that this evaluation approach is\ninappropriate. For that aim, we reconsider data for the samples with $x = 0.96$\nand $x = 1.02$ from three different perspectives: (i) analysis of the\nlogarithmic temperature derivative of the conductivity, (ii) study of the\ndeviations of the measured conductivity data from the Al'tshuler-Aronov\napproximation of the temperature dependence, and (iii) comparison of the\nmeasured temperature data with the values obtained treating the sample as\nsecondary thermometer in terms of that approximation.\n This way, for the sample with $x = 0.96$, classified as metallic by Daichi\nOka et al., qualitative contradictions between the measurements and the\nzero-temperature extrapolation according to the Al'tshuler-Aronov theory are\nuncovered. Thus, this sample very likely exhibits activated instead of metallic\nconduction. In consequence, our findings question the continuity of the MIT\nresulting from the highly cited scaling theory of localization.", "category": "cond-mat_dis-nn" }, { "text": "Random-field-induced disordering mechanism in a disordered ferromagnet:\n Between the Imry-Ma and the standard disordering mechanism: Random fields disorder Ising ferromagnets by aligning single spins in the\ndirection of the random field in three space dimensions, or by flipping large\nferromagnetic domains at dimensions two and below. While the former requires\nrandom fields of typical magnitude similar to the interaction strength, the\nlatter Imry-Ma mechanism only requires infinitesimal random fields. Recently,\nit has been shown that for dilute anisotropic dipolar systems a third mechanism\nexists, where the ferromagnetic phase is disordered by finite-size glassy\ndomains at a random field of finite magnitude that is considerably smaller than\nthe typical interaction strength. Using large-scale Monte Carlo simulations and\nzero-temperature numerical approaches, we show that this mechanism applies to\ndisordered ferromagnets with competing short-range ferromagnetic and\nantiferromagnetic interactions, suggesting its generality in ferromagnetic\nsystems with competing interactions and an underlying spin-glass phase. A\nfinite-size-scaling analysis of the magnetization distribution suggests that\nthe transition might be first order.", "category": "cond-mat_dis-nn" }, { "text": "High-dimensional order parameters and neural network classifiers applied\n to amorphous ices: Amorphous ice phases are key constituents of water's complex structural\nlandscape. This study investigates the polyamorphic nature of water, focusing\non the complexities within low-density amorphous ice (LDA), high-density\namorphous ice (HDA), and the recently discovered medium-density amorphous ice\n(MDA). We use rotationally-invariant, high-dimensional order parameters to\ncapture a wide spectrum of local symmetries for the characterisation of local\noxygen environments. We train a neural network (NN) to classify these local\nenvironments, and investigate the distinctiveness of MDA within the structural\nlandscape of amorphous ice. Our results highlight the difficulty in accurately\ndifferentiating MDA from LDA due to structural similarities. Beyond water, our\nmethodology can be applied to investigate the structural properties and phases\nof disordered materials.", "category": "cond-mat_dis-nn" }, { "text": "Bistable Gradient Networks II: Storage Capacity and Behaviour Near\n Saturation: We examine numerically the storage capacity and the behaviour near saturation\nof an attractor neural network consisting of bistable elements with an\nadjustable coupling strength, the Bistable Gradient Network (BGN). For strong\ncoupling, we find evidence of a first-order \"memory blackout\" phase transition\nas in the Hopfield network. For weak coupling, on the other hand, there is no\nevidence of such a transition and memorized patterns can be stable even at high\nlevels of loading. The enhanced storage capacity comes, however, at the cost of\nimperfect retrieval of the patterns from corrupted versions.", "category": "cond-mat_dis-nn" }, { "text": "Vortex characterisation of frustration in the 2d Ising spin glass: The frustrated Ising model on a two-dimensional lattice with open boundary\nconditions is revisited. A hidden Z2 gauge symmetry relates models with\ndifferent frustrations which, however, share the same partition function. By\nmeans of a duality transformation, it is shown that the partition function only\ndepends on the distribution of gauge invariant vortices on the lattice. We\nfinally show that the exact ground state energy can be calculated in polynomial\ntime using Edmonds' algorithm.", "category": "cond-mat_dis-nn" }, { "text": "Correlation between vibrational anomalies and emergent anharmonicity of\n local potential energy landscape in metallic glasses: The boson peak (BP) is a universal feature in the Raman and inelastic\nscattering spectra of both disordered and crystalline materials. The current\nparadigm presents the boson peak as the result of a Ioffe-Regel crossover\nbetween ballistic (phonon) and diffusive-type excitations, where the loss of\ncoherence of phonons is described as a purely harmonic process due to\nstructural disorder. This \"harmonic disorder\" paradigm for the BP has never\nbeen challenged or tested at the atomistic level. Here, through a set of\natomistically-resolved characterizations of amorphous metallic alloys, we\nuncover a robust inverse proportionality between the intensity of boson peak\nand the activation energy of excitations in the potential energy landscape\n(PEL). Larger boson peak is linked with shallower basins and lower activation\nbarriers and, consequently, with strongly anharmonic sectors of the PEL.\nNumerical evidence from atomistic simulations indicates that THz atomic\nvibrations contributing the most to the BP in atomic glasses are strongly\nanharmonic, as evidenced through very large values of the atomic- and\nmode-resolved Gr\\\"{u}neisen parameter found for the atomic vibrations that\nconstitute the BP. These results provide a direct bridge between the\nvibrational spectrum and the topology of the PEL in solids, and point towards a\nnew \"giant anharmonicity\" paradigm for both generic disordered materials and\nfor the phonon-glass problem in emerging materials for energy applications. In\nthis sense, disorder and anharmonicity emerge as the two sides of the same\ncoin.", "category": "cond-mat_dis-nn" }, { "text": "Understanding the problem of glass transition on the basis of elastic\n waves in a liquid: We propose that the properties of glass transition can be understood on the\nbasis of elastic waves. Elastic waves originating from atomic jumps in a liquid\npropagate local expansion due to the anharmonicity of interatomic potential.\nThis creates dynamic compressive stress, which increases the activation barrier\nfor other events in a liquid. The non-trivial point is that the range of\npropagation of high-frequency elastic waves, $d_{\\rm el}$, increases with\nliquid relaxation time $\\tau$. A self-consistent calculation shows that this\nincrease gives the Vogel-Fulcher-Tammann (VFT) law. In the proposed theory, we\ndiscuss the origin of two dynamic crossovers in a liquid: 1) the crossover from\nexponential to non-exponential and from Arrhenius to VFT relaxation at high\ntemperature and 2) the crossover from the VFT to a more Arrhenius-like\nrelaxation at low temperature. The corresponding values of $\\tau$ at the two\ncrossovers are in quantitative parameter-free agreement with experiments. The\norigin of the second crossover allows us to reconcile the ongoing controversy\nsurrounding the possible divergence of $\\tau$. The crossover to Arrhenius\nrelaxation universally takes place when $d_{\\rm el}$ reaches system size, thus\navoiding divergence and associated theoretical complications such as\nidentifying the nature of the phase transition and the second phase itself.\nFinally, we discuss the effect of volume on $\\tau$ and the origin of liquid\nfragility.", "category": "cond-mat_dis-nn" }, { "text": "Photocount statistics in mesoscopic optics: We report the first observation of the impact of mesoscopic fluctuations on\nthe photocount statistics of coherent light scattered in a random medium.\nPoisson photocount distribution of the incident light widens and gains\nadditional asymmetry upon transmission through a suspension of small dielectric\nspheres. The effect is only appreciable when the average number of\nphotocounts becomes comparable or larger than the effective dimensionless\nconductance g of the sample.", "category": "cond-mat_dis-nn" }, { "text": "Strain localisation above the yielding point in cyclically deformed\n glasses: We study the yielding behaviour of a model glass under cyclic athermal\nquastistatic deformation computationally, and show that yielding is\ncharacterised by the discontinuous appearance of shear bands, whose width is\nabout ten particle diameters at their initiation, in which the strain gets\nlocalised. Strain localisation is accompanied by a corresponding change in the\nenergies, and a decrease in the density in the shear band. We show that the\nglass remains well annealed outside the shear band whereas the energies\ncorrespond to the highest possible energy minima at the given density within\nthe shear band. Diffusive motion of particles characterising the yielded state\nare confined to the shear bands, whose mean positions display movement over\nrepeated cycles. Outside the shear band, particle motions are sub-diffusive but\nremain finite. Despite the discontinuous nature of their appearance, shear\nbands are reversible in the sense that a reduction in the amplitude of cyclic\ndeformation to values below yielding leads to the healing and disappearance of\nthe shear bands.", "category": "cond-mat_dis-nn" }, { "text": "Glass and jamming transition of simple liquids: static and dynamic\n theory: We study the glass and jamming transition of finite-dimensional models of\nsimple liquids: hard- spheres, harmonic spheres and more generally bounded pair\npotentials that modelize frictionless spheres in interaction. At finite\ntemperature, we study their glassy dynamics via field-theoretic methods by\nresorting to a mapping towards an effective quantum mechanical evolution, and\nshow that such an approach resolves several technical problems encountered with\nprevious attempts. We then study the static, mean-field version of their glass\ntransition via replica theory, and set up an expansion in terms of the\ncorresponding static order parameter. Thanks to this expansion, we are able to\nmake a direct and exact comparison between historical Mode-Coupling results and\nreplica theory. Finally we study these models at zero temperature within the\nhypotheses of the random-first-order-transition theory, and are able to derive\na quantitative mean-field theory of the jamming transition. The theoretic\nmethods of field theory and liquid theory used in this work are presented in a\nmostly self-contained, and hopefully pedagogical, way. This manuscript is a\ncorrected version of my PhD thesis, defended in June, 29th, under the\nadvisorship of Fr\\'ed\\'eric van Wijland, and also contains the result of\ncollaborations with Ludovic Berthier and Francesco Zamponi. The PhD work was\nfunded by a CFM-JP Aguilar grant, and conducted in the Laboratory MSC at\nUniversit\\'e Denis Diderot--Paris 7, France.", "category": "cond-mat_dis-nn" }, { "text": "Relation between heterogeneous frozen regions in supercooled liquids and\n non-Debye spectrum in the corresponding glasses: Recent numerical studies on glassy systems provide evidences for a population\nof non-Goldstone modes (NGMs) in the low-frequency spectrum of the vibrational\ndensity of states $D(\\omega)$. Similarly to Goldstone modes (GMs), i. e.,\nphonons in solids, NGMs are soft low-energy excitations. However, differently\nfrom GMs, NGMs are localized excitations. Here we first show that the parental\ntemperature $T^*$ modifies the GM/NGM ratio in $D(\\omega)$. In particular, the\nphonon attenuation is reflected in a parental temperature dependency of the\nexponent $s(T^*)$ in the low-frequency power law $D(\\omega) \\sim\n\\omega^{s(T^*)}$, with $2 \\leq s(T^*) \\leq 4 $. Secondly, by comparing $s(T^*)$\nwith $s(p)$, i. e., the same quantity obtained by pinning \\mttp{a} $p$ particle\nfraction, we suggest that $s(T^*)$ reflects the presence of dynamical\nheterogeneous regions of size $\\xi^3 \\propto p$. Finally, we provide an\nestimate of $\\xi$ as a function of $T^*$, finding a mild power law divergence,\n$\\xi \\sim (T^* - T_d)^{-\\alpha/3}$, with $T_d$ the dynamical crossover\ntemperature and $\\alpha$ falling in the range $\\alpha \\in [0.8,1.0]$.", "category": "cond-mat_dis-nn" }, { "text": "Localization dynamics in a centrally coupled system: In systems where interactions couple a central degree of freedom and a bath,\none would expect signatures of the bath's phase to be reflected in the dynamics\nof the central degree of freedom. This has been recently explored in connection\nwith many-body localized baths coupled with a central qubit or a single cavity\nmode -- systems with growing experimental relevance in various platforms. Such\nmodels also have an interesting connection with Floquet many-body localization\nvia quantizing the external drive, although this has been relatively\nunexplored. Here we adapt the multilayer multiconfigurational time-dependent\nHartree (ML-MCTDH) method, a well-known tree tensor network algorithm, to\nnumerically simulate the dynamics of a central degree of freedom, represented\nby a $d$-level system (qudit), coupled to a disordered interacting 1D spin\nbath. ML-MCTDH allows us to reach $\\approx 10^2$ lattice sites, a far larger\nsystem size than what is feasible with exact diagonalization or kernel\npolynomial methods. From the intermediate time dynamics, we find a well-defined\nthermodynamic limit for the qudit dynamics upon appropriate rescaling of the\nsystem-bath coupling. The spin system shows similar scaling collapse in the\nEdward-Anderson spin glass order parameter or entanglement entropy at\nrelatively short times. At longer time scales, we see slow growth of the\nentanglement, which may arise from dephasing mechanisms in the localized system\nor long-range interactions mediated by the central degree of freedom. Similar\nsigns of localization are shown to appear as well with unscaled system-bath\ncoupling.", "category": "cond-mat_dis-nn" }, { "text": "Ordering temperatures of Ising Spin Glasses: Exploiting an approach due to Singh and Fisher I show that in the high\ndimension limit the ordering temperature of near neighbour Ising Spin Glasses\ndrops linearly with the kurtosis of the interaction distribution, in excellent\nagreement with accurate high temperature series data of Daboul, Chang and\nAharony. At lower dimensions the linear relation no longer applies strictly but\nthe kurtosis can still be taken to be an appropriate parameter for ranking\ndifferent systems. I also compare the series estimates with simulation and\nMigdal-Kadanoff estimates where these are available.", "category": "cond-mat_dis-nn" }, { "text": "Roughness and critical force for depinning at 3-loop order: A $d$-dimensional elastic manifold at depinning is described by a\nrenormalized field theory, based on the Functional Renormalization Group (FRG).\nHere we analyze this theory to 3-loop order, equivalent to third order in\n$\\epsilon=4-d$, where $d$ is the internal dimension. The critical exponent\nreads $\\zeta = \\frac \\epsilon3 + 0.04777 \\epsilon^2 -0.068354 \\epsilon^3 +\n{\\cal O}(\\epsilon^4)$. Using that $\\zeta(d=0)=2^-$, we estimate\n$\\zeta(d=1)=1.266(20)$, $\\zeta(d=2)=0.752(1)$ and $\\zeta(d=3)=0.357(1)$. For\nGaussian disorder, the pinning force per site is estimated as $f_{\\rm c}= {\\cal\nB} m^{2}\\rho_m + f_{\\rm c}^0$, where $m^2$ is the strength of the confining\npotential, $\\cal B$ a universal amplitude, $\\rho_m$ the correlation length of\nthe disorder, and $f_{\\rm c}^0$ a non-universal lattice dependent term. For\ncharge-density waves, we find a mapping to the standard $\\phi^4$-theory with\n$O(n)$ symmetry in the limit of $n\\to -2$. This gives $f_{\\rm c} = \\tilde {\\cal\nA}(d) m^2 \\ln (m) + f_{\\rm c}^0 $, with $\\tilde {\\cal A}(d) = -\\partial_n\n\\big[\\nu(d,n)^{-1}+\\eta(d,n)\\big]_{n=-2}$, reminiscent of log-CFTs.", "category": "cond-mat_dis-nn" }, { "text": "Spectral statistics across the many-body localization transition: The many-body localization transition (MBLT) between ergodic and many-body\nlocalized phase in disordered interacting systems is a subject of much recent\ninterest. Statistics of eigenenergies is known to be a powerful probe of\ncrossovers between ergodic and integrable systems in simpler examples of\nquantum chaos. We consider the evolution of the spectral statistics across the\nMBLT, starting with mapping to a Brownian motion process that analytically\nrelates the spectral properties to the statistics of matrix elements. We\ndemonstrate that the flow from Wigner-Dyson to Poisson statistics is a\ntwo-stage process. First, fractal enhancement of matrix elements upon\napproaching the MBLT from the metallic side produces an effective power-law\ninteraction between energy levels, and leads to a plasma model for level\nstatistics. At the second stage, the gas of eigenvalues has local interaction\nand level statistics belongs to a semi-Poisson universality class. We verify\nour findings numerically on the XXZ spin chain. We provide a microscopic\nunderstanding of the level statistics across the MBLT and discuss implications\nfor the transition that are strong constraints on possible theories.", "category": "cond-mat_dis-nn" }, { "text": "Normal and anomalous diffusion of Brownian particles on disordered\n potentials: In this work we study the transition from normal to anomalous diffusion of\nBrownian particles on disordered potentials. The potential model consists of a\nseries of \"potential hills\" (defined on unit cell of constant length) whose\nheights are chosen randomly from a given distribution. We calculate the exact\nexpression for the diffusion coefficient in the case of uncorrelated potentials\nfor arbitrary distributions. We particularly show that when the potential\nheights have a Gaussian distribution (with zero mean and a finite variance) the\ndiffusion of the particles is always normal. In contrast when the distribution\nof the potential heights are exponentially distributed we show that the\ndiffusion coefficient vanishes when system is placed below a critical\ntemperature. We calculate analytically the diffusion exponent for the anomalous\n(subdiffusive) phase by using the so-called \"random trap model\". We test our\npredictions by means of Langevin simulations obtaining good agreement within\nthe accuracy of our numerical calculations.", "category": "cond-mat_dis-nn" }, { "text": "Robustness and Independence of the Eigenstates with respect to the\n Boundary Conditions across a Delocalization-Localization Phase Transition: We focus on the many-body eigenstates across a localization-delocalization\nphase transition. To characterize the robustness of the eigenstates, we\nintroduce the eigenstate overlaps $\\mathcal{O}$ with respect to the different\nboundary conditions. In the ergodic phase, the average of eigenstate overlaps\n$\\bar{\\mathcal{O}}$ is exponential decay with the increase of the system size\nindicating the fragility of its eigenstates, and this can be considered as an\neigenstate-version butterfly effect of the chaotic systems. For localized\nsystems, $\\bar{\\mathcal{O}}$ is almost size-independent showing the strong\nrobustness of the eigenstates and the broken of eigenstate thermalization\nhypothesis. In addition, we find that the response of eigenstates to the change\nof boundary conditions in many-body localized systems is identified with the\nsingle-particle wave functions in Anderson localized systems. This indicates\nthat the eigenstates of the many-body localized systems, as the many-body wave\nfunctions, may be independent of each other. We demonstrate that this is\nconsistent with the existence of a large number of quasilocal integrals of\nmotion in the many-body localized phase. Our results provide a new method to\nstudy localized and delocalized systems from the perspective of eigenstates.", "category": "cond-mat_dis-nn" }, { "text": "Percolation through Voids around Overlapping Spheres, a Dynamically\n based Finite Size Scaling Analysis: The percolation threshold for flow or conduction through voids surrounding\nrandomly placed spheres is rigorously calculated. With large scale Monte Carlo\nsimulations, we give a rigorous continuum treatment to the geometry of the\nimpenetrable spheres and the spaces between them. To properly exploit finite\nsize scaling, we examine multiple systems of differing sizes, with suitable\naveraging over disorder, and extrapolate to the thermodynamic limit. An order\nparameter based on the statistical sampling of stochastically driven dynamical\nexcursions and amenable to finite size scaling analysis is defined, calculated\nfor various system sizes, and used to determine the critical volume fraction\nphi_{c} = 0.0317 +/- 0.0004 and the correlation length exponent nu = 0.92 +/-\n0.05.", "category": "cond-mat_dis-nn" }, { "text": "Fragility and molar volumes of non-stoichiometric chalcogenides -- the\n crucial role of melt/glass homogenization: Melt-fragility index (m) and glass molar volumes (Vm) of binary Ge-Se\nmelts/glasses are found to change reproducibly as they are homogenized.\nVariance of Vm decreases as glasses homogenize, and the mean value of Vm\nincreases to saturate at values characteristic of homogeneous glasses. Variance\nin fragility index of melts also decreases as they are homogenized, and the\nmean value of m decreases to acquire values characteristic of homogeneous\nmelts. Broad consequences of these observations on physical behavior of\nchalcogenides melts/glasses are commented upon. The intrinsically slow kinetics\nof melt homogenization derives from high viscosity of select super-strong melt\ncompositions in the Intermediate Phase that serve to bottleneck atomic\ndiffusion at high temperatures.", "category": "cond-mat_dis-nn" }, { "text": "Recovering the state sequence of hidden Markov models using mean-field\n approximations: Inferring the sequence of states from observations is one of the most\nfundamental problems in Hidden Markov Models. In statistical physics language,\nthis problem is equivalent to computing the marginals of a one-dimensional\nmodel with a random external field. While this task can be accomplished through\ntransfer matrix methods, it becomes quickly intractable when the underlying\nstate space is large.\n This paper develops several low-complexity approximate algorithms to address\nthis inference problem when the state space becomes large. The new algorithms\nare based on various mean-field approximations of the transfer matrix. Their\nperformances are studied in detail on a simple realistic model for DNA\npyrosequencing.", "category": "cond-mat_dis-nn" }, { "text": "Surface properties at the Kosterlitz-Thouless transition: Monte Carlo simulations of the two-dimensional XY model are performed in a\nsquare geometry with free and mixed fixed-free boundary conditions. Using a\nSchwarz-Christoffel conformal mapping, we deduce the exponent eta of the order\nparameter correlation function and its surface equivalent eta_parallel at the\nKosterlitz-Thouless transition temperature. The well known value eta(T_{KT}) =\n1/4 is easily recovered even with systems of relatively small sizes, since the\nshape effects are encoded in the conformal mapping. The exponent associated to\nthe surface correlations is similarly obtained eta_1(T_{KT}) ~= 0.54.", "category": "cond-mat_dis-nn" }, { "text": "Universality in short-range Ising spin glasses: The role of the distribution of coupling constants on the critical exponents\nof the short-range Ising spin-glass model is investigated via real space\nrenormalization group. A saddle-point spin glass critical point characterized\nby a fixed-point distribution is found in an appropriated parameter space. The\ncritical exponents $\\beta $ and $\\nu $ are directly estimated from the data of\nthe local Edwards-Anderson order parameters for the model defined on a diamond\nhierarchical lattice of fractal dimension $d_{f}=3$. Four distinct initial\ndistributions of coupling constants (Gaussian, bimodal, uniform and\nexponential) are considered; the results clearly indicate a universal behavior.", "category": "cond-mat_dis-nn" }, { "text": "Coherent wave transmission in quasi-one-dimensional systems with L\u00e9vy\n disorder: We study the random fluctuations of the transmission in disordered\nquasi-one-dimensional systems such as disordered waveguides and/or quantum\nwires whose random configurations of disorder are characterized by density\ndistributions with a long tail known as L\\'evy distributions. The presence of\nL\\'evy disorder leads to large fluctuations of the transmission and anomalous\nlocalization, in relation to the standard exponential localization (Anderson\nlocalization). We calculate the complete distribution of the transmission\nfluctuations for different number of transmission channels in the presence and\nabsence of time-reversal symmetry. Significant differences in the transmission\nstatistics between disordered systems with Anderson and anomalous localizations\nare revealed. The theoretical predictions are independently confirmed by tight\nbinding numerical simulations.", "category": "cond-mat_dis-nn" }, { "text": "Comment on the possibility of Inverse Crystallization within van\n Hemmen's Classical Spin-Glass model: In this comment, I show that van Hemmen's classical spin-glass model can also\naccount for processes such as inverse crystallization, where a ferromagnetic\nphase appears at higher temperatures than a glass state. The so far ignored\nfact is the temperature dependence of the Ruderman-Kittel-Kasuya-Yosida\ninteraction. This generalization may be relevant to other models.", "category": "cond-mat_dis-nn" }, { "text": "Broadband dielectric spectroscopy on benzophenone: alpha relaxation,\n beta relaxation, and mode coupling theory: We have performed a detailed dielectric investigation of the relaxational\ndynamics of glass-forming benzophenone. Our measurements cover a broad\nfrequency range of 0.1 Hz to 120 GHz and temperatures from far below the glass\ntemperature well up into the region of the small-viscosity liquid. With respect\nto the alpha relaxation this material can be characterized as a typical\nmolecular glass former with rather high fragility. A good agreement of the\nalpha relaxation behavior with the predictions of the mode coupling theory of\nthe glass transition is stated. In addition, at temperatures below and in the\nvicinity of Tg we detect a well-pronounced beta relaxation of Johari-Goldstein\ntype, which with increasing temperature develops into an excess wing. We\ncompare our results to literature data from optical Kerr effect and depolarized\nlight scattering experiments, where an excess-wing like feature was observed in\nthe 1 - 100 GHz region. We address the question if the Cole-Cole peak, which\nwas invoked to describe the optical Kerr effect data within the framework of\nthe mode coupling theory, has any relation to the canonical beta relaxation\ndetected by dielectric spectroscopy.", "category": "cond-mat_dis-nn" }, { "text": "Moving binary Bose-Einstein condensates in a weak random potential: We study the behavior of moving Bose-Bose mixtures in a weak disordered\npotential in the realm of the Bogoliubov-Huang-Meng theory. Corrections due to\nthe quantum fluctuations, disorder effects and the relative motion of two\nfluids to the glassy fraction, the condensed depletion, the anomalous density,\nand the equation of state of each species are obtained analytically for small\nvelocity. We show that the intriguing interplay of the relative motion and the\ndisorder potential could not only change the stability condition, but destroy\nalso the localization process in the two condensates preventing the formation\nof a Bose glass state. Unexpectedly, we find that the quantum fluctuations\nreduce with the velocity of the two fluids. The obtained theoretical\npredictions are checked by our numerical results.", "category": "cond-mat_dis-nn" }, { "text": "Learning to find order in disorder: We introduce the use of neural networks as classifiers on classical\ndisordered systems with no spatial ordering. In this study, we implement a\nconvolutional neural network trained to identify the spin-glass state in the\nthree-dimensional Edwards-Anderson Ising spin-glass model from an input of\nMonte Carlo sampled configurations at a given temperature. The neural network\nis designed to be flexible with the input size and can accurately perform\ninference over a small sample of the instances in the test set. Using the\nneural network to classify instances of the three-dimensional Edwards-Anderson\nIsing spin-glass in a (random) field we show that the inferred phase boundary\nis consistent with the absence of an Almeida-Thouless line.", "category": "cond-mat_dis-nn" }, { "text": "Triviality of the Ground State Structure in Ising Spin Glasses: We investigate the ground state structure of the three-dimensional Ising spin\nglass in zero field by determining how the ground state changes in a fixed\nfinite block far from the boundaries when the boundary conditions are changed.\nWe find that the probability of a change in the block ground state\nconfiguration tends to zero as the system size tends to infinity. This\nindicates a trivial ground state structure, as predicted by the droplet theory.\nSimilar results are also obtained in two dimensions.", "category": "cond-mat_dis-nn" }, { "text": "Barkhausen noise in the Random Field Ising Magnet Nd$_2$Fe$_{14}$B: With sintered needles aligned and a magnetic field applied transverse to its\neasy axis, the rare-earth ferromagnet Nd$_2$Fe$_{14}$B becomes a\nroom-temperature realization of the Random Field Ising Model. The transverse\nfield tunes the pinning potential of the magnetic domains in a continuous\nfashion. We study the magnetic domain reversal and avalanche dynamics between\nliquid helium and room temperatures at a series of transverse fields using a\nBarkhausen noise technique. The avalanche size and energy distributions follow\npower-law behavior with a cutoff dependent on the pinning strength dialed in by\nthe transverse field, consistent with theoretical predictions for Barkhausen\navalanches in disordered materials. A scaling analysis reveals two regimes of\nbehavior: one at low temperature and high transverse field, where the dynamics\nare governed by the randomness, and the second at high temperature and low\ntransverse field where thermal fluctuations dominate the dynamics.", "category": "cond-mat_dis-nn" }, { "text": "Renormalization-Group Theory of 1D quasiperiodic lattice models with\n commensurate approximants: We develop a renormalization group (RG) description of the localization\nproperties of onedimensional (1D) quasiperiodic lattice models. The RG flow is\ninduced by increasing the unit cell of subsequent commensurate approximants.\nPhases of quasiperiodic systems are characterized by RG fixed points associated\nwith renormalized single-band models. We identify fixed-points that include\nmany previously reported exactly solvable quasiperiodic models. By classifying\nrelevant and irrelevant perturbations, we show that phase boundaries of more\ngeneric models can be determined with exponential accuracy in the approximant's\nunit cell size, and in some cases analytically. Our findings provide a unified\nunderstanding of widely different classes of 1D quasiperiodic systems.", "category": "cond-mat_dis-nn" }, { "text": "Band-center metal-insulator transition in bond-disordered graphene: We study the transport properties of a tight-binding model of non-interacting\nfermions with random hopping on the honeycomb lattice. At the particle-hole\nsymmetric chemical potential, the absence of diagonal disorder (random onsite\npotentials) places the system in the well-studied chiral orthogonal\nuniversality class of disordered fermion problems, which are known to exhibit\nboth a critical metallic phase and a dimerization-induced localized phase.\nHere, our focus is the behavior of the two-terminal conductance and the\nLyapunov spectrum in quasi-1D geometry near the dimerization-driven transition\nfrom the metallic to the localized phase. For a staggered dimerization pattern\non the square and honeycomb lattices, we find that the renormalized\nlocalization length $\\xi/M$ ($M$ denotes the width of the sample) and the\ntypical conductance display scaling behavior controlled by a crossover\nlength-scale that diverges with exponent $\\nu \\approx 1.05(5)$ as the critical\npoint is approached. However, for the plaquette dimerization pattern, we\nobserve a relatively large exponent $\\nu \\approx 1.55(5)$ revealing an apparent\nnon-universality of the delocalization-localization transition in the BDI\nsymmetry class.", "category": "cond-mat_dis-nn" }, { "text": "Dynamics of a quantum phase transition in the Aubry-Andr\u00e9-Harper\n model with $p$-wave superconductivity: We investigate the nonequilibrium dynamics of the one-dimension\nAubry-Andr\\'{e}-Harper model with $p$-wave superconductivity by changing the\npotential strength with slow and sudden quench. Firstly, we study the slow\nquench dynamics from localized phase to critical phase by linearly decreasing\nthe potential strength $V$. The localization length is finite and its scaling\nobeys the Kibble-Zurek mechanism. The results show that the second-order phase\ntransition line shares the same critical exponent $z\\nu$, giving the\ncorrelation length $\\nu=0.997$ and dynamical exponent $z=1.373$, which are\ndifferent from the Aubry-Andr\\'{e} model. Secondly, we also study the sudden\nquench dynamics between three different phases: localized phase, critical\nphase, and extended phase. In the limit of $V=0$ and $V=\\infty$, we\nanalytically study the sudden quench dynamics via the Loschmidt echo. The\nresults suggest that, if the initial state and the post-quench Hamiltonian are\nin different phases, the Loschmidt echo vanishes at some time intervals.\nFurthermore, we found that, if the initial value is in the critical phase, the\ndirection of the quench is the same as one of the two limits mentioned before,\nand similar behaviors will occur.", "category": "cond-mat_dis-nn" }, { "text": "Coulomb Glasses: A Comparison Between Mean Field and Monte Carlo Results: Recently a local mean field theory for both eqilibrium and transport\nproperties of the Coulomb glass was proposed [A. Amir et al., Phys. Rev. B 77,\n165207 (2008); 80, 245214 (2009)]. We compare the predictions of this theory to\nthe results of dynamic Monte Carlo simulations. In a thermal equilibrium state\nwe compare the density of states and the occupation probabilities. We also\nstudy the transition rates between different states and find that the mean\nfield rates underestimate a certain class of important transitions. We propose\nmodified rates to be used in the mean field approach which take into account\ncorrelations at the minimal level in the sense that transitions are only to\ntake place from an occupied to an empty site. We show that this modification\naccounts for most of the difference between the mean field and Monte Carlo\nrates. The linear response conductance is shown to exhibit the Efros-Shklovskii\nbehaviour in both the mean field and Monte Carlo approaches, but the mean field\nmethod strongly underestimates the current at low temperatures. When using the\nmodified rates better agreement is achieved.", "category": "cond-mat_dis-nn" }, { "text": "Spin Wave Propagation in the Domain State of a Random Field Magnet: Inelastic neutron scattering with high wave-vector resolution has\ncharacterized the propagation of transverse spin wave modes near the\nantiferromagnetic zone center in the metastable domain state of a random field\nIsing magnet. A well-defined, long wavelength excitation is observed despite\nthe absence of long-range magnetic order. Direct comparisons with the spin wave\ndispersion in the long-range ordered antiferromagnetic state reveal no\nmeasurable effects from the domain structure. This result recalls analogous\nbehavior in thermally disordered anisotropic spin chains but contrasts sharply\nwith that of the phonon modes in relaxor ferroelectrics.", "category": "cond-mat_dis-nn" }, { "text": "On the Approach to the Equilibrium and the Equilibrium Properties of a\n Glass-Forming Model: In this note we apply some theoretical predictions that arise in the mean\nfield framework for a large class of infinite range models to structural\nglasses and we present a first comparison of these predictions with numerical\nresults.", "category": "cond-mat_dis-nn" }, { "text": "A Simple Model for Simple Aging in Glassy Yttrium-Hydrides: A simple explanation for the logarithmic aging of the photoconductivity in\nyttriumhydride is proposed. We show that the scaling (``simple'' aging) of the\nrelaxation response with the illumination time t_w is consistent with the\nsuperposition of independently relaxing excitations with time offsets\ndistributed over a window of width t_w.", "category": "cond-mat_dis-nn" }, { "text": "Pinning dependent field driven domain wall dynamics and thermal scaling\n in an ultrathin Pt/Co/Pt magnetic film: Magnetic field-driven domain wall motion in an ultrathin Pt/Co(0.45nm)/Pt\nferromagnetic film with perpendicular anisotropy is studied over a wide\ntemperature range. Three different pinning dependent dynamical regimes are\nclearly identified: the creep, the thermally assisted flux flow and the\ndepinning, as well as their corresponding crossovers. The wall elastic energy\nand microscopic parameters characterizing the pinning are determined. Both the\nextracted thermal rounding exponent at the depinning transition, $\\psi=$0.15,\nand the Larkin length crossover exponent, $\\phi=$0.24, fit well with the\nnumerical predictions.", "category": "cond-mat_dis-nn" }, { "text": "Entropy and typical properties of Nash equilibria in two-player games: We use techniques from the statistical mechanics of disordered systems to\nanalyse the properties of Nash equilibria of bimatrix games with large random\npayoff matrices. By means of an annealed bound, we calculate their number and\nanalyse the properties of typical Nash equilibria, which are exponentially\ndominant in number. We find that a randomly chosen equilibrium realizes almost\nalways equal payoffs to either player. This value and the fraction of\nstrategies played at an equilibrium point are calculated as a function of the\ncorrelation between the two payoff matrices. The picture is complemented by the\ncalculation of the properties of Nash equilibria in pure strategies.", "category": "cond-mat_dis-nn" }, { "text": "Learning and inference in a nonequilibrium Ising model with hidden nodes: We study inference and reconstruction of couplings in a partially observed\nkinetic Ising model. With hidden spins, calculating the likelihood of a\nsequence of observed spin configurations requires performing a trace over the\nconfigurations of the hidden ones. This, as we show, can be represented as a\npath integral. Using this representation, we demonstrate that systematic\napproximate inference and learning rules can be derived using dynamical\nmean-field theory. Although naive mean-field theory leads to an unstable\nlearning rule, taking into account Gaussian corrections allows learning the\ncouplings involving hidden nodes. It also improves learning of the couplings\nbetween the observed nodes compared to when hidden nodes are ignored.", "category": "cond-mat_dis-nn" } ]