Marginally stable phases in mean-field structural glasses

TL;DR

This paper maps out the phase diagrams of mean-field structural glasses, revealing conditions under which different glasses become marginally stable, with implications for experiments on colloids, foams, and molecular glasses.

Contribution

It provides comprehensive phase diagrams for marginal stability across various interactions and conditions, unifying previous models and guiding future experiments.

Findings

All types of glasses can become marginally stable.

Extent of marginal stability depends on preparation protocol.

Predicted observable marginal phases in colloids and poorly annealed glasses.

Abstract

A novel form of amorphous matter characterized by marginal stability was recently discovered in the mean-field theory of structural glasses. Using this approach, we provide complete phase diagrams delimiting the location of the marginally stable glass phase for a large variety of pair interactions and physical conditions, extensively exploring physical regimes relevant to granular matter, foams, emulsions, hard and soft colloids, and molecular glasses. We find that all types of glasses may become marginally stable, but the extent of the marginally stable phase highly depends on the preparation protocol. Our results suggest that marginal phases should be observable for colloidal and non-Brownian particles near jamming, and poorly annealed glasses. For well-annealed glasses, two distinct marginal phases are predicted. Our study unifies previous results on marginal stability in mean-field models, and will be useful to guide numerical simulations and experiments aimed at detecting marginal stability in finite dimensional amorphous materials.