Hopping and the Stokes-Einstein relation breakdown in simple glass formers

TL;DR

This paper investigates how particle hopping affects the breakdown of the Stokes-Einstein relation in glass formers, revealing that hopping modifies but does not entirely disrupt the mean-field glass transition scenario.

Contribution

It introduces a framework combining multiple theoretical and simulation methods to isolate and quantify the role of hopping in glassy dynamics, advancing understanding of finite-dimensional effects.

Findings

Hopping causes a breakdown of the Stokes-Einstein relation.

Hopping supersedes the dynamical glass transition.

A sizable critical regime remains unaffected by hopping.

Abstract

One of the most actively debated issues in the study of the glass transition is whether a mean-field description is a reasonable starting point for understanding experimental glass formers. Although the mean-field theory of the glass transition -- like that of other statistical systems -- is exact when the spatial dimension $d\rightarrow\infty$, the evolution of systems properties with $d$ may not be smooth. Finite-dimensional effects could dramatically change what happens in physical dimensions, $d=2,3$. For standard phase transitions finite-dimensional effects are typically captured by renormalization group methods, but for glasses the corrections are much more subtle and only partially understood. Here, we investigate hopping between localized cages formed by neighboring particles in a model that allows to cleanly isolate that effect. By bringing together results from replica theory, cavity reconstruction, void percolation, and molecular dynamics, we obtain insights into how hopping induces a breakdown of the Stokes--Einstein relation and modifies the mean-field scenario in experimental systems. Although hopping is found to supersede the dynamical glass transition, it nonetheless leaves a sizable part of the critical regime untouched. By providing a constructive framework for identifying and quantifying the role of hopping, we thus take an important step towards describing dynamic facilitation in the framework of the mean-field theory of glasses.