相关论文: Glassy Random Matrix Models

We present a new solution of the asymmetric two-matrix model in the large $N$ limit which only involves a saddle point analysis. The model can be interpreted as Ising in the presence of a magnetic field, on random dynamical lattices with…

The leading correction to the smoothed connected energy density-density correlation function is obtained for the large energy difference, within the context of the Gaussian Random Matrix Theory. In order to achieve this result, the…

We solve a supersymmetric matrix model with a general potential. While matrix models usually describe surfaces, supersymmetry enforces a cancellation of bosonic and fermionic loops and only diagrams corresponding to so-called branched…

We present a three-dimensional lattice-gas model with trivial thermodynamics, but nontrivial dynamics. The model is characterized by each particle having its own random energy landscape. The equilibrium dynamics of the model were…

Magnetizations are introduced to the Generalized Random Energy Model (GREM) and numerical simulations on ac susceptibility is made for direct comparison with experiments in glassy materials. Prominent dynamical natures of spin glasses, {\it…

We consider the critical properties of points of continuous glass transition as one can find in liquids in presence of constraints or in liquids in porous media. Through a one loop analysis we show that the critical Replica Field Theory…

The existence of a constant density of two-level systems (TLS) was proposed as the basis of some intriguing universal aspects of glasses at ultra-low temperatures. Here we ask whether their existence is necessary for explaining the…

Multiple orthogonal polynomials are a generalization of orthogonal polynomials in which the orthogonality is distributed among a number of orthogonality weights. They appear in random matrix theory in the form of special determinantal point…

We introduce a new disordered system, the Super-Potts model, which is a more frustrated version of the Potts glass. Its elementary degrees of freedom are variables that can take M values and are coupled via pair-wise interactions. Its exact…

We consider the two matrix model with an even quartic potential W(y)=y^4/4+alpha y^2/2 and an even polynomial potential V(x). The main result of the paper is the formulation of a vector equilibrium problem for the limiting mean density for…

This paper summarizes some work I've been doing on eigenvalue correlators of Random Matrix Models which show some interesting behaviour. First we consider matrix models with gaps in there spectrum or density of eigenvalues. The…

The barriers between metastable states near the glass transition of a random heteropolymer are studied using replicas by describing inhomogeneous states. The instanton solution for a replica space free energy functional is found numerically…

It is well known that the joint probability density of the eigenvalues of Gaussian ensembles of random matrices may be interpreted as a Coulomb gas. We review these classical results for hermitian and complex random matrices, with special…

We take on a Random Matrix theory viewpoint to study the spectrum of certain reversible Markov chains in random environment. As the number of states tends to infinity, we consider the global behavior of the spectrum, and the local behavior…

Some puzzles which arise in matrix models with multiple cuts are presented. They are present in the smoothed eigenvalue correlators of these models. First a method is described to calculate smoothed eigenvalue correlators in random matrix…

We investigate the energy landscape of two dimensional network models for covalent glasses by means of the lid algorithm. For three different particle densities and for a range of network sizes, we exhaustively analyse many configuration…

We review the nature of glass transitions and the glasses arising from a square-well potential with a narrow and deep well. Our discussion is based on the Mode Coupling Theory, and the predictions of glasses that we make refer to the…

In this paper, we consider a class of models for multiphase fluids, in the framework of mixture theory. The considered system, in its more general form, contains both the gradient of a hydrostatic pressure, generated by an incompressibility…

Using a distinguishable-particle lattice model based on void-induced dynamics, we successfully reproduce the well-known linear relation between heat capacity and temperature at very low temperatures. The heat capacity is dominated by…

We present a simple model for an associating liquid in which polymorphism and density anomaly are connected. Our model combines a two dimensional lattice gas with particles interacting through a soft core potential and orientational degrees…