相关论文: Mean Field Model of a Glass

We investigate the liquid-glass phase transition in a system of point-like particles interacting via a finite-range attractive potential in D-dimensional space. The phase transition is driven by an `entropy crisis' where the available phase…

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…

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…

We investigate a toy model of liquid, based on simplified HNC equations in very large spatial dimension D. The model does not exhibit a phase transition, but several regimes of the behavior when D\to\infty can be observed in different…

The study of the properties of glass-forming liquids is difficult for many reasons. Analytic solutions of mean field models are usually available only for systems embedded in a space with an unphysically high number of spatial dimensions;…

We propose a novel model for a glass-forming liquid which allows to switch in a continuous manner from a standard three-dimensional liquid to a fully connected mean-field model. This is achieved by introducing k additional particle-particle…

In this letter we study a lattice gas system that undergoes a glassy transition. When we approach the glass transition we find both a divergence of a point to set correlation length and the vanishing of the thermodynamic potential. These…

A quantitative application to real supercooled liquids of the mean-field scenario for the glass transition ($T_g$) is proposed. This scenario, based on an analogy with spin-glass models, suggests a unified picture of the mode-coupling…

The exact mean-field theory for the simplest glass-forming system - the dense assembly of hard spheres in the large dimensional limit - predicts the existence of a Gardner phase. This transition is characterized by full replica symmetry…

We study the glass and jamming transition of finite-dimensional models of simple liquids: hard- spheres, harmonic spheres and more generally bounded pair potentials that modelize frictionless spheres in interaction. At finite temperature,…

We discuss thermotropic nematic liquid crystals in the mean-field regime. In the first part of this article, we rigorously carry out the mean-field limit of a system of $N$ rod-like particles as $N\to\infty$, which yields an effective…

We study the low temperature phase of the 3D Coulomb glass within a mean field approach which reduces the full problem to an effective single site model with a non-trivial replica structure. We predict a finite glass transition temperature…

We propose a simple theory for the dynamics of model glass-forming fluids, which should be solvable using a mean-field-like approach. The theory is based on transparent physical assumptions, which can be tested in computer simulations. The…

Often the current mode coupling theory (MCT) of glass transitions is compared with mean field theories. We explore this possible correspondence. After showing a simple-minded derivation of MCT with some difficulties we give a concise…

We construct a mean field theory for the lattice model of a structural glass and solve it using the replica method and one step replica symmetry breaking ansatz; this theory becomes exact in the limit of infinite dimensions. Analyzing…

By using numerical simulations we show that the 4D $J=\pm 1$ Edwards Anderson spin glass in magnetic field undergoes a mean field like phase transition. We use a dynamical approach: we simulate large lattices (of volume $V$) and work out…

Mean-field models of glasses that present a random first order transition exhibit highly non-trivial fluctuations. Building on previous studies that focused on the critical scaling regime, we here obtain a fully quantitative framework for…

In this paper we expand our previous investigation of a quantum particle subject to the action of a random potential plus a fixed harmonic potential at a finite temperature T. In the classical limit the system reduces to a well-known…

A full mean field solution of a quantum Heisenberg spin glass model is presented in a large-N limit. A spin glass transition is found for all values of the spin S. The quantum critical regime associated with the quantum transition at S=0,…

We propose a method to study quantitatively the glass transition in a system of interacting particles. In spite of the absence of any quenched disorder, we introduce a replicated version of the hypernetted chain equations. The solution of…