Mean-field glass transition in a model liquid

TL;DR

This paper analytically studies the liquid-glass transition in a model of particles with finite-range attraction, revealing an entropy crisis characterized by a discontinuous order parameter but continuous free energy.

Contribution

It provides a first-principles replica calculation of the mean-field liquid-glass transition in a finite-range attractive particle system.

Findings

Identification of an entropy crisis at the transition

Finite jump in the order parameter

Continuous free energy and first derivative at transition

Abstract

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 space volume collapses dramatically at the transition. We describe the general strategy underlying the first-principles replica calculation for this type of transition; its application to our model system then allows for an analytic description of the liquid-glass phase transition within a mean-field approximation, provided the parameters are chosen suitably. We find a transition exhibiting all the features associated with an `entropy crisis', including the characteristic finite jump of the order parameter at the transition while the free energy and its first derivative remain continuous.