A mean-field hard-spheres model of glass

TL;DR

This paper introduces a high-dimensional mean-field model of hard spheres to study glassy behavior, combining analytical diagrammatic expansion and numerical simulations to explore the transition to a glassy regime at high pressures.

Contribution

It develops a novel mean-field model of hard spheres in high dimensions and connects it to matrix models, providing new insights into glass formation and high-pressure regimes.

Findings

Evidence of a glassy regime at high pressures

Successful analytical diagrammatic expansion of the matrix model

Numerical simulations support the theoretical predictions

Abstract

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 diagrammatic expansion of this matrix model. Finally, we show the results from numerical simulations and we present evidence for a glassy regime at high pressures.