Mean Field Model of a Glass

TL;DR

This paper introduces a mean-field toy model for the liquid-glass transition using a system of particles with infinite-range oscillating interactions, demonstrating a phase transition via replica symmetry breaking.

Contribution

It presents a novel simplified mean-field model capturing the liquid-glass phase transition with a clear theoretical framework.

Findings

System exhibits a phase transition between liquid and glass phases.

Transition characterized by one-step replica symmetry breaking.

Model provides insights into the nature of the glass transition.

Abstract

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 potential. In the framework of the replica approach it is shown that such a system exhibits the phase transition between the high-temperature liquid phase and the low-temperature glass phase. This phase transition is described in terms of the standard one-step replica symmetry breaking scheme.