Dynamical transition of glasses: from exact to approximate

TL;DR

This paper introduces a family of glassy models with a tunable interaction range, bridging exact mean-field descriptions and finite-dimensional systems, revealing that mean-field behavior approximates three-dimensional glasses well even at short ranges.

Contribution

It develops a new family of models interpolating between finite-dimensional and mean-field glasses, providing a dynamic virial construction and insights into the validity of mean-field approximations.

Findings

Mean-field behavior closely follows for interaction ranges as small as one interparticle distance in 3D.

The models suggest mean-field theory becomes more accurate at higher dimensions.

The approach offers a new perspective on the dynamical transition in glasses.

Abstract

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 exactly described by equations conceptually close, but different from, the Mode-Coupling equations. We obtain these by a dynamic virial construction. Quite surprisingly we observe that in three dimensions, the mean-field behavior is closely followed for ranges as small as one interparticle distance, and still qualitatively for smaller distances. For the original particle model, we expect the present mean-field theory to become, unlike the Mode-Coupling equations, an increasingly good approximation at higher dimensions.