Related papers: On the mean field approach to glassy systems
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…
These lecture notes focus on the mean field theory of spin glasses, with particular emphasis on the presence of a very large number of metastable states in these systems. This phenomenon, and some of its physical consequences, will be…
We introduce a family of glassy models having a parameter, playing the role of an interaction range, that may be varied continuously to go from a system of particles in d dimensions to a mean-field version of it. The mean-field limit is…
We discuss mean field theory of glasses without quenched disorder focusing on the justification of the replica approach to thermodynamics. We emphasize the assumptions implicit in this method and discuss how they can be verified. The…
We study statistical properties of peculiar responses in glassy systems at mesoscopic scales based on a class of mean-field spin-glass models which exhibit 1 step replica symmetry breaking. Under variation of a generic external field, a…
Here I will review the theoretical results that have been obtained for spin glasses. I will concentrate my attention on the predictions of the mean field approach in three dimensional systems and on its numerical and experimental…
In this note I present a simplified version of the recent computation (Mezard and Parisi 1998, 1999) of the properties of glasses in the low temperature phase in the framework of the replica theory, using an extension of the tools used in…
In talk I will review the theoretical results that have been obtained for spin glasses, paying a particular attention to finite dimensional spin glasses. I will concentrate my attention on the formulation of the mean field approach and on…
In this talk, after a short phenomenological introduction on glasses, I will describe some recent progresses that have been done in glasses using the replica method in the definition and in the evaluation of the configurational entropy (or…
The analytical model of a glass-forming system is formulated within the formalism analogous to gauge theory constructions in quantum field theory. This work explores the scope of the proposed approach and investigates the equilibrium…
We discuss the mean-field theory of spin-glass models with frustrated long-range random spin exchange. We analyze the reasons for breakdown of the simple mean-field theory of Sherrington and Kirkpatrick. We relate the replica-symmetry…
The behavior of a family of mean-field glass models is reviewed. The models are analyzed by means of a Langevin-based approach to the dynamics and a Replica theory computation of the thermodynamics. We focus on the phase diagram of a…
The aim of this report is to review a theoretical approach that has been proposed recently to describe dynamic fluctuations in glassy systems (work in collaboration with H. Castillo, C. Chamon, P. Charbonneau, J. L. Iguain, M. Kennett, D.…
Many mean-field models have been introduced to describe the mechanical behavior of glassy materials. They often rely on averages performed over distributions of elements or states. We here underline that averaging is a more intricate…
In this paper we propose a simple mean-field "toy" model for the liquid-glass phase transition. This is the system of $N$ point-like particles confined in a finite volume of a $D$-dimensional space interacting via infinite-range oscillating…
In this talk I present some of the recent theoretical results that have been obtained on glassy systems like spin glasses or structural glasses. The physical principles at the basis of the theory are explained in a simple language (without…
The concept of replica symmetry breaking found in the solution of the mean-field Sherrington-Kirkpatrick spin-glass model has been applied to a variety of problems in science ranging from biological to computational and even financial…
Important gaps remain in our understanding of the thermodynamics and statistical physics of self-gravitating systems. Using mean field theory, here we investigate the equilibrium properties of several spherically symmetric model systems…
In the present paper we analyze the critical properties of a quantum spherical spin glass model with short range, random interactions. Since the model allows for rigorous detailed calculations, we can show how the effective partition…
Spherical symmetry is ubiquitous in nature. It's therefore unfortunate that spherical system simulations are so hard, and require complete spheres with millions of interacting particles. Here we introduce an approach to model spherical…