相关论文: Glassy Random Matrix Models

This is a first step in counting the number of multiple solutions in certain glassy random matrix models introduced in refs. \cite{d02}. We are able to do this by reducing the problem of counting the multiple solutions to that of a moment…

A random matrix approach to glassy physics is introduced. It leads to a class of models which exhibit both, glassy low-temperature phases, and double-- and single-well configurations in their potential energy. The distribution of parameters…

We study symmetry breaking in $Z_2$ symmetric large $N$ matrix models. In the planar approximation for both the symmetric double-well $\phi^4$ model and the symmetric Penner model, we find there is an infinite family of broken symmetry…

We consider an invariant random matrix model where the standard Gaussian potential is distorted by an additional single pole of order $m$. We compute the average or macroscopic spectral density in the limit of large matrix size, solving the…

The Chiral Random Matrix Model or the Gaussian Penner Model (generalized Laguerre ensemble) is re-examined in the light of the results which have been found in double well matrix models [D97,BD99] and subtleties discovered in the single…

We present a family of solvable models of interacting particles in high dimensionalities without quenched disorder. We show that the models have a glassy regime with aging effects. The interaction is controlled by a parameter $p$. For $p=2$…

We consider the random matrix model with external source, in case where the potential V(x) is an even polynomial and the external source has two eigenvalues a, -a of equal multiplicity. We show that the limiting mean eigenvalue distribution…

An analytically tractable model is introduced which exhibits both, a glass--like freezing transition, and a collection of double--well configurations in its zero--temperature potential energy landscape. The latter are generally believed to…

Geo-materials such as vuggy carbonates are known to exhibit multiple spatial scales. A common manifestation of spatial scales is the presence of (at least) two different scales of pores, which is commonly referred to as double porosity. To…

Tensor models play an increasingly prominent role in many fields, notably in machine learning. In several applications, such as community detection, topic modeling and Gaussian mixture learning, one must estimate a low-rank signal from a…

A theoretical analysis [Angelani et al., Phys. Rev. Lett. 96, 065702 (2006)] predicts glassy behaviour of light in a nonlinear random medium. This implies slow dynamics related to the presence of many metastable states. We consider very…

We introduce a Potts model with quenched, frustrated disorder, that enjoys of a gauge symmetry that forbids spontaneous magnetization, and allows the glassy phase to extend from $T_c$ down to T=0. We study numerical the 4 dimensional model…

The richness of the mean-field solution of simple glasses leaves many of its features challenging to interpret. A minimal model that illuminates glass physics the same way the random energy model clarifies spin glass behavior would…

We propose a microscopic translationally invariant glass model which exhibits two level tunneling systems with a broad range of asymmetries and barrier heights in its glassy phase. Their distribution is qualitatively different from what is…

Multiple distinct glass states occur in binary hard-sphere mixtures with constituents of very disparate sizes according to the mode-coupling theory of the glass transition (MCT), distinguished by considering whether small particles remain…

We present a model of spheres moving in a high-dimensional compact space. We relate it to a mixed matrix model with a $O(N)$ invariant model plus a $P(N)$ invariant perturbation. We then study the low pressure regime by performing a…

In this paper we present an exact study of the relaxation dynamics of the backgammon model. This is a model of a gas of particles in a discrete space which presents glassy phenomena as a result of {\it entropy barriers} in configuration…

A quadratic extension of REM has been treated. Discussed here is the origin of relation of REM to strings and other complex physical phenomena. Two basic features of the REM class of complex phenomena were identified: the double…

This work finds its place in the statistical mechanical approach to light amplification in disordered media, namely Random Lasers (RLs). The problem of going beyond the standard mean-field Replica Symmetry Breaking (RSB) theory employed to…

We consider a product of an arbitrary number of independent rectangular Gaussian random matrices. We derive the mean densities of its eigenvalues and singular values in the thermodynamic limit, eventually verified numerically. These…