Glassy dynamics: mean-field `landscape' pictures versus growing length scale scenarii

TL;DR

This paper reviews the compatibility of mean-field landscape theories with the concept of a growing cooperative length scale in understanding glassy dynamics, highlighting unresolved questions about glass non-flow.

Contribution

It clarifies the relationship between mean-field potential energy landscape models and real-space cooperative length scales in glass transition theories.

Findings

Mean-field theories naturally incorporate potential energy landscapes.

Growing length scales are essential to describe glassy slowing down.

Outstanding questions remain about the non-flow behavior of glasses.

Abstract

This is a short review on the compatibility between (a) mean-field, mode-coupling theories of the glass transition, where potential energy landscape ideas are natural, and (b) the necessity of describing the slowing down of glassy materials in terms of a growing cooperative length, absent from mean-field descriptions. We summarize some of the outstanding questions that remain before we can say we understand why glasses do not flow.