Using mutual information to measure order in model glass-formers

TL;DR

This paper employs mutual information to quantify amorphous order in glass-formers, revealing that static order does not grow significantly without crystalline order, while dynamic correlations increase rapidly with density.

Contribution

It introduces mutual information as a novel, general measure of amorphous order sensitive to multi-particle correlations in glassy systems.

Findings

Little growth of amorphous order without crystalline order.

Dynamic correlation length increases faster than static length with density.

Recovers known scaling in kinetically constrained models.

Abstract

Whether or not there is growing static order accompanying the dynamical heterogeneity and increasing relaxation times seen in glassy systems is a matter of dispute. An obstacle to resolving this issue is that the order is expected to be amorphous and so not amenable to simple order parameters. We use mutual information to provide a general measurement of order that is sensitive to multi-particle correlations. We apply this to two glass-forming systems (2D binary mixtures of hard disks with different size ratios to give varying amounts of hexatic order) and show that there is little growth of amorphous order in the system without crystalline order. In both cases we measure the dynamical length with a four-point correlation function and find that it increases significantly faster than the static lengths in the system as density is increased. We further show that we can recover the known scaling of the dynamic correlation length in a kinetically constrained model, the 2-TLG.