On the solution of a `solvable' model of an ideal glass of hard spheres displaying a jamming transition

TL;DR

This paper analytically solves a mean field model of hard spheres that exhibits both an ideal glass transition and jamming points, providing insights into the glass and jamming phenomena.

Contribution

It introduces an analytical solution of a mean field model with both glass transition and jamming, and compares approximate and exact methods for finite dimensions.

Findings

Analytical equations describing the model are established.

Approximate solutions and numerical strategies are compared.

Insights into the reliability of the theory for finite-dimensional systems are obtained.

Abstract

We discuss the analytical solution through the cavity method of a mean field model that displays at the same time an ideal glass transition and a set of jamming points. We establish the equations describing this system, and we discuss some approximate analytical solutions and a numerical strategy to solve them exactly. We compare these methods and we get insight into the reliability of the theory for the description of finite dimensional hard spheres.