Glass and Jamming Transitions: From Exact Results to Finite-Dimensional Descriptions

TL;DR

This paper reviews recent theoretical and numerical advances in understanding amorphous materials, focusing on mean-field solutions and their relevance to finite-dimensional systems, especially regarding jamming and glass transitions.

Contribution

It synthesizes exact mean-field results with finite-dimensional simulations, highlighting robust features and sensitivities in the physics of glasses and jamming.

Findings

Mean-field solutions are robust in finite dimensions.

Finite-dimensional simulations confirm some mean-field predictions.

Identifies sensitive features in the glass and jamming transitions.

Abstract

Despite decades of work, gaining a first-principle understanding of amorphous materials remains an extremely challenging problem. However, recent theoretical breakthroughs have led to the formulation of an exact solution in the mean-field limit of infinite spatial dimension, and numerical simulations have remarkably confirmed the dimensional robustness of some of the predictions. This review describes these latest advances. More specifically, we consider the dynamical and thermodynamic descriptions of hard spheres around the dynamical, Gardner and jamming transitions. Comparing mean-field predictions with the finite-dimensional simulations, we identify robust aspects of the description and uncover its more sensitive features. We conclude with a brief overview of ongoing research.