The Gardner transition in physical dimensions

TL;DR

This paper investigates the Gardner transition in physical systems, revealing that some features attributed to it are artifacts and that the transition becomes an avoided transition with large correlation lengths in a quasi-one-dimensional setup.

Contribution

It demonstrates that certain features of the Gardner transition are artifacts and provides evidence of an avoided transition with large correlation lengths in a simplified model.

Findings

Features of the Gardner transition can be artifacts due to local cage escapes.

The Gardner transition becomes an avoided transition with large correlation length (~15 diameters).

Features associated with the Gardner transition are observed in a narrow channel disk system.

Abstract

The Gardner transition is the transition that at mean-field level separates a stable glass phase from a marginally stable phase. This transition has similarities with the de Almeida-Thouless transition of spin glasses. We have studied a well-understood problem, that of disks moving in a narrow channel, which shows many features usually associated with the Gardner transition. However, we can show that some of these features are artifacts that arise when a disk escapes its local cage during the quench to higher densities. There is evidence that the Gardner transition becomes an avoided transition, in that the correlation length becomes quite large, of order 15 particle diameters, even in our quasi-one-dimensional system.