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arXiv2014

Suppression of tunneling two-level systems in ultrastable glasses of indomethacin

Glasses and other non-crystalline solids exhibit thermal and acoustic properties at low temperatures anomalously different from those found in crystalline solids, and with a remarkable degree of universality. Below a few K, these universal properties have been successfully interpreted using the Tunneling Model, which has enjoyed (almost) unanimous recognition for decades. Here we present low-temperature specific-heat measurements of ultrastable glasses of indomethacin that clearly show the disappearance of the ubiquitous linear contribution traditionally ascribed to the existence of tunneling two-level systems (TLS). When the ultrastable thin-film sample is thermally converted into a conventional glass, the material recovers a typical amount of TLS. This remarkable suppression of the TLS found in ultrastable glasses of indomethacin is argued to be due to their particular anisotropic and layered character, which strongly influences the dynamical network and may hinder isotropic interactions among low-energy defects, rather than to the thermodynamic stabilization itself. This explanation may lend support to the criticisms by Leggett and others to the standard Tunneling Model, although more experiments in different kinds of ultrastable glasses are needed to ascertain this hypothesis.

cond-mat.dis-nn↗

arXiv2014

A novel approach to numerical measurements of the configurational entropy in supercooled liquids

The configurational entropy is among the key observables to characterize experimentally the formation of a glass. Physically, it quantifies the multiplicity of metastable states in which an amorphous material can be found at a given temperature, and its temperature dependence provides a major thermodynamic signature of the glass transition, which is experimentally accessible. Measurements of the configurational entropy require, however, some approximations which have often led to ambiguities and contradictory results. Here we implement a novel numerical scheme to measure the configurational entropy Sigma(T) in supercooled liquids, using a direct determination of the free energy cost to localize the system within a single metastable state at temperature T. For two prototypical glass-forming liquids, we find that Sigma(T) disappears discontinuously above a temperature T_c, which is slightly lower than the usual estimate of the onset temperature for glassy dynamics. This observation is in good agreement with theoretical expectations, but contrasts sharply with alternative numerical methods. While the temperature dependence of Sigma(T) correlates with the glass fragility, we show that the validity of the Adam-Gibbs relation (relating configurational entropy to structural relaxation time) established in earlier numerical studies is smaller than previously thought, potentially resolving an important conflict between experiments and simulations.

cond-mat.stat-mech↗

arXiv2014

Acoustic excitations and elastic heterogeneities in disordered solids

In the recent years, much attention has been devoted to the inhomogeneous nature of the mechanical response at the nano-scale in disordered solids. Clearly, the elastic heterogeneities that have been characterized in this context are expected to strongly impact the nature of the sound waves which, in contrast to the case of perfect crystals, cannot be completely rationalized in terms of phonons. Building on previous work on a toy model showing an amorphisation transition [Mizuno H, Mossa S, Barrat JL (2013) EPL {\bf 104}:56001], we investigate the relationship between sound waves and elastic heterogeneities in a unified framework, by continuously interpolating from the perfect crystal, through increasingly defective phases, to fully developed glasses. We provide strong evidence of a direct correlation between sound waves features and the extent of the heterogeneous mechanical response at the nano-scale.

cond-mat.dis-nn↗

arXiv2014

Hopping and the Stokes-Einstein relation breakdown in simple glass formers

One of the most actively debated issues in the study of the glass transition is whether a mean-field description is a reasonable starting point for understanding experimental glass formers. Although the mean-field theory of the glass transition -- like that of other statistical systems -- is exact when the spatial dimension $d\rightarrow\infty$, the evolution of systems properties with $d$ may not be smooth. Finite-dimensional effects could dramatically change what happens in physical dimensions, $d=2,3$. For standard phase transitions finite-dimensional effects are typically captured by renormalization group methods, but for glasses the corrections are much more subtle and only partially understood. Here, we investigate hopping between localized cages formed by neighboring particles in a model that allows to cleanly isolate that effect. By bringing together results from replica theory, cavity reconstruction, void percolation, and molecular dynamics, we obtain insights into how hopping induces a breakdown of the Stokes--Einstein relation and modifies the mean-field scenario in experimental systems. Although hopping is found to supersede the dynamical glass transition, it nonetheless leaves a sizable part of the critical regime untouched. By providing a constructive framework for identifying and quantifying the role of hopping, we thus take an important step towards describing dynamic facilitation in the framework of the mean-field theory of glasses.

cond-mat.dis-nn↗

arXiv2018

Support for the value 5/2 for the spin glass lower critical dimension at zero magnetic field

We study numerically various properties of the free energy barriers in the Edwards-Anderson model of spin glasses in the low-temperature region both in three and four spatial dimensions. In particular, we investigated the dependence of height of free energy barriers on system size and on the distance between the initial and final states (i.e. the overlap distance). A related quantity is the distribution of large local fluctuations of the overlap in large three-dimensional samples at equilibrium. Our results for both quantities (barriers and large deviations) are in agreement with the prediction obtained in the framework of mean field theory. In addition, our result supports $D_{lc}=2.5$ as the lower critical dimension for the model.

cond-mat.dis-nn↗

arXiv2018

Optimal Errors and Phase Transitions in High-Dimensional Generalized Linear Models

Generalized linear models (GLMs) arise in high-dimensional machine learning, statistics, communications and signal processing. In this paper we analyze GLMs when the data matrix is random, as relevant in problems such as compressed sensing, error-correcting codes or benchmark models in neural networks. We evaluate the mutual information (or "free entropy") from which we deduce the Bayes-optimal estimation and generalization errors. Our analysis applies to the high-dimensional limit where both the number of samples and the dimension are large and their ratio is fixed. Non-rigorous predictions for the optimal errors existed for special cases of GLMs, e.g. for the perceptron, in the field of statistical physics based on the so-called replica method. Our present paper rigorously establishes those decades old conjectures and brings forward their algorithmic interpretation in terms of performance of the generalized approximate message-passing algorithm. Furthermore, we tightly characterize, for many learning problems, regions of parameters for which this algorithm achieves the optimal performance, and locate the associated sharp phase transitions separating learnable and non-learnable regions. We believe that this random version of GLMs can serve as a challenging benchmark for multi-purpose algorithms. This paper is divided in two parts that can be read independently: The first part (main part) presents the model and main results, discusses some applications and sketches the main ideas of the proof. The second part (supplementary informations) is much more detailed and provides more examples as well as all the proofs.

cs.IT↗

arXiv2018

A random critical point separates brittle and ductile yielding transitions in amorphous materials

We combine an analytically solvable mean-field elasto-plastic model with molecular dynamics simulations of a generic glass-former to demonstrate that, depending on their preparation protocol, amorphous materials can yield in two qualitatively distinct ways. We show that well-annealed systems yield in a discontinuous brittle way, as metallic and molecular glasses do. Yielding corresponds in this case to a first-order nonequilibrium phase transition. As the degree of annealing decreases, the first-order character becomes weaker and the transition terminates in a second-order critical point in the universality class of an Ising model in a random field. For even more poorly annealed systems, yielding becomes a smooth crossover, representative of the ductile rheological behavior generically observed in foams, emulsions, and colloidal glasses. Our results show that the variety of yielding behavior found in amorphous materials does not result from the diversity of particle interactions or microscopic dynamics {\it per se}, but is instead unified by carefully considering the role of the initial stability of the system.

cond-mat.dis-nn↗

arXiv2018

Universality of jamming of non-spherical particles

Amorphous packings of non-spherical particles such as ellipsoids and spherocylinders are known to be hypostatic: the number of mechanical contacts between particles is smaller than the number of degrees of freedom, thus violating Maxwell's mechanical stability criterion. In this work, we propose a general theory of hypostatic amorphous packings and the associated jamming transition. First, we show that many systems fall into a same universality class. As an example, we explicitly map ellipsoids into a system of `breathing' particles. We show by using a marginal stability argument that in both cases jammed packings are hypostatic, and that the critical exponents related to the contact number and the vibrational density of states are the same. Furthermore, we introduce a generalized perceptron model which can be solved analytically by the replica method. The analytical solution predicts critical exponents in the same hypostatic jamming universality class. Our analysis further reveals that the force and gap distributions of hypostatic jamming do not show power-law behavior, in marked contrast to the isostatic jamming of spherical particles. Finally, we confirm our theoretical predictions by numerical simulations.

cond-mat.dis-nn↗

arXiv2019

Shaping the Branched Flow of Light through Disordered Media

Electronic matter waves traveling through the weak and smoothly varying disorder potential of a semi-conductor show branching behavior instead of a smooth spreading of flow. By transferring this phenomenon to optics, we show how the branched flow of light can be controlled to propagate along a single branch rather than through many of them at the same time. Our method is based on shaping the incoming wavefront and only requires partial knowledge of the system's transmission matrix. We show that the light flowing along a single branch has a broadband frequency stability such that we can even steer pulses along selected branches - a prospect with many interesting possibilities for wave control in disordered environments.

physics.optics↗

arXiv2013

Persistence and First-Passage Properties in Non-equilibrium Systems

In this review we discuss the persistence and the related first-passage properties in extended many-body nonequilibrium systems. Starting with simple systems with one or few degrees of freedom, such as random walk and random acceleration problems, we progressively discuss the persistence properties in systems with many degrees of freedom. These systems include spins models undergoing phase ordering dynamics, diffusion equation, fluctuating interfaces etc. Persistence properties are nontrivial in these systems as the effective underlying stochastic process is non-Markovian. Several exact and approximate methods have been developed to compute the persistence of such non-Markov processes over the last two decades, as reviewed in this article. We also discuss various generalisations of the local site persistence probability. Persistence in systems with quenched disorder is discussed briefly. Although the main emphasis of this review is on the theoretical developments on persistence, we briefly touch upon various experimental systems as well.

cond-mat.stat-mech↗

arXiv2018

Spontaneous synchronization and nonequilibrium statistical mechanics of coupled phase oscillators

Spontaneous synchronization is a remarkable collective effect observed in nature, whereby a population of oscillating units, which have diverse natural frequencies and are in weak interaction with one another, evolves to spontaneously exhibit collective oscillations at a common frequency. The Kuramoto model provides the basic analytical framework to study spontaneous synchronization. The model comprises limit-cycle oscillators with distributed natural frequencies interacting through a mean-field coupling. Although more than forty years have passed since its introduction, the model continues to occupy the centre-stage of research in the field of non-linear dynamics, and is also widely applied to model diverse physical situations. In this brief review, starting with a derivation of the Kuramoto model and the synchronization phenomenon it exhibits, we summarize recent results on the study of a generalized Kuramoto model that includes inertial effects and stochastic noise. We describe the dynamics of the generalized model from a different yet a rather useful perspective, namely, that of long-range interacting systems driven out of equilibrium by quenched disordered external torques. A system is said to be long-range interacting if the inter-particle potential decays slowly as a function of distance. Using tools of statistical physics, we highlight the equilibrium and nonequilibrium aspects of the dynamics of the generalized Kuramoto model, and uncover a rather rich and complex phase diagram that it exhibits, which underlines the basic theme of intriguing emergent phenomena that are exhibited by many-body complex systems.

nlin.AO↗

arXiv2019

Prediction on Elastic Properties of Nb-doped Ni Systems

On the basis of the first principles simulation, the structure, formation enthalpy, and mechanical properties (elastic constant, bulk, and shear modulus and hardness) of five Nb-doped Ni systems are systematically studied. The calculated equilibrium volume increases with the Nb concentration increasing. The computational elastic constants and formation enthalpy indicate that all Nb-doped Ni systems are mechanically and thermodynamically stable in our research. The hardness of these systems also be predicted after the bulk modulus and shear modulus have been accurately calculated. The results show that the hardness increases with the Nb concentration increasing when the Nb concentration below 4.9%, beyond which the hardness will decrease within the scope of our study.

cond-mat.mtrl-sci↗

arXiv2011

Ground States of the Sherrington-Kirkpatrick Spin Glass with Levy Bonds

Ground states of Ising spin glasses on fully connected graphs are studied for a broadly distributed bond family. In particular, bonds $J$ distributed according to a Levy distribution P(J)\propto 1/|J|^{1+α}, |J|>1, are investigated for a range of powers α. The results are compared with those for the Sherrington-Kirkpatrick (SK) model, where bonds are Gaussian distributed. In particular, we determine the variation of the ground state energy densities with α, their finite-size corrections, measure their fluctuations, and analyze the local field distribution. We find that the energies themselves at infinite system size attain universally the Parisi-energy of the SK as long as the second moment of P(J) exists (α>2), and compare favorably with recent one-step replica symmetry breaking predictions well below α=2. At and just below α=2, the simulations deviate significantly from theoretical expectations. The finite-size investigation reveals that the corrections exponent ωdecays from the SK value ω_{SK}=2/3 already well above α=2, at which point it reaches a minimum. This result is justified with a speculative calculation of a random energy model with Levy bonds. The exponent ρthat describes the variations of the ground state energy fluctuations with system size decays monotonically from its SK value over the entire range of αand apparently vanishes at α=1.

cond-mat.dis-nn↗

arXiv2011

Ising model for distribution networks

An elementary Ising spin model is proposed for demonstrating cascading failures (break-downs, blackouts, collapses, avalanches, ...) that can occur in realistic networks for distribution and delivery by suppliers to consumers. A ferromagnetic Hamiltonian with quenched random fields results from policies that maximize the gap between demand and delivery. Such policies can arise in a competitive market where firms artificially create new demand, or in a solidary environment where too high a demand cannot reasonably be met. Network failure in the context of a policy of solidarity is possible when an initially active state becomes metastable and decays to a stable inactive state. We explore the characteristics of the demand and delivery, as well as the topological properties, which make the distribution network susceptible of failure. An effective temperature is defined, which governs the strength of the activity fluctuations which can induce a collapse. Numerical results, obtained by Monte Carlo simulations of the model on (mainly) scale-free networks, are supplemented with analytic mean-field approximations to the geometrical random field fluctuations and the thermal spin fluctuations. The role of hubs versus poorly connected nodes in initiating the breakdown of network activity is illustrated and related to model parameters.

physics.soc-ph↗

arXiv2012

Density of states and extent of wave function: two crucial factors for small polaron hopping conductivity in 1D

We introduce a theoretical model to scrutinize the conductivity of small polarons in one-dimensional disordered systems, focusing on two crucial --as will be demonstrated-- factors: the density of states and the spatial extent of the electronic wave function. The investigation is performed for any temperature up to 300 K and under electric field of arbitrary strength up to the polaron dissociation limit. To accomplish this task we combine analytical work with numerical calculations.

cond-mat.dis-nn↗

arXiv2011

State sampling dependence of the Hopfield network inference

The fully connected Hopfield network is inferred based on observed magnetizations and pairwise correlations. We present the system in the glassy phase with low temperature and high memory load. We find that the inference error is very sensitive to the form of state sampling. When a single state is sampled to compute magnetizations and correlations, the inference error is almost indistinguishable irrespective of the sampled state. However, the error can be greatly reduced if the data is collected with state transitions. Our result holds for different disorder samples and accounts for the previously observed large fluctuations of inference error at low temperatures.

cond-mat.dis-nn↗

arXiv2019

Active online learning in the binary perceptron problem

The binary perceptron is the simplest artificial neural network formed by $N$ input units and one output unit, with the neural states and the synaptic weights all restricted to $\pm 1$ values. The task in the teacher--student scenario is to infer the hidden weight vector by training on a set of labeled patterns. Previous efforts on the passive learning mode have shown that learning from independent random patterns is quite inefficient. Here we consider the active online learning mode in which the student designs every new Ising training pattern. We demonstrate that it is mathematically possible to achieve perfect (error-free) inference using only $N$ designed training patterns, but this is computationally unfeasible for large systems. We then investigate two Bayesian statistical designing protocols, which require $2.3 N$ and $1.9 N$ training patterns, respectively, to achieve error-free inference. If the training patterns are instead designed through deductive reasoning, perfect inference is achieved using $N\!+\!\log_{2}\!N$ samples. The performance gap between Bayesian and deductive designing strategies may be shortened in future work by taking into account the possibility of ergodicity breaking in the version space of the binary perceptron.

cs.LG↗

arXiv2013

Traffic data reconstruction based on Markov random field modeling

We consider the traffic data reconstruction problem. Suppose we have the traffic data of an entire city that are incomplete because some road data are unobserved. The problem is to reconstruct the unobserved parts of the data. In this paper, we propose a new method to reconstruct incomplete traffic data collected from various traffic sensors. Our approach is based on Markov random field modeling of road traffic. The reconstruction is achieved by using mean-field method and a machine learning method. We numerically verify the performance of our method using realistic simulated traffic data for the real road network of Sendai, Japan.

stat.ML↗