Dimensional Study of the Caging Order Parameter at the Glass Transition

TL;DR

This study investigates the shape of the caging order parameter at the glass transition across dimensions, revealing deviations from Gaussian assumptions and highlighting limitations in current mean-field theories.

Contribution

It demonstrates that the cage shape remains non-Gaussian in the mean-field limit, challenging existing theoretical assumptions and suggesting revisions for better experimental alignment.

Findings

Cage shape remains non-trivial across dimensions

Mean-field theories miss crucial cage shape details

Non-mean-field corrections are small as dimension decreases

Abstract

The glass problem is notoriously hard and controversial. Even at the mean-field level, little is agreed about how a fluid turns sluggish while exhibiting but unremarkable structural changes. It is clear, however, that the process involves self-caging, which provides an order parameter for the transition. It is also broadly assumed that this cage should have a Gaussian shape in the mean-field limit. Here we show that this ansatz does not hold. By performing simulations as a function of spatial dimension, we find the cage to keep a non-trivial form. Quantitative mean-field descriptions of the glass transition, such as mode-coupling theory, density functional theory, and replica theory, all miss this crucial element. Although the mean-field random first-order transition scenario of the glass transition is here qualitatively supported and non-mean-field corrections are found to remain small on decreasing dimension, reconsideration of its implementation is needed for it to result in a coherent description of experimental observations.