Numerical detection of the Gardner transition in a mean-field glass former

TL;DR

This paper numerically detects the Gardner transition in a mean-field glass model using three independent methods, confirming theoretical predictions and suggesting applicability to real systems.

Contribution

It introduces robust numerical approaches to identify the Gardner transition in a simple structural glass model, aligning with theoretical expectations.

Findings

Transition point identified by divergence of relaxation time

Divergence of caging susceptibility observed

Abnormal tail in cage order parameter distribution

Abstract

Recent theoretical advances predict the existence, deep into the glass phase, of a novel phase transition, the so-called Gardner transition. This transition is associated with the emergence of a complex free energy landscape composed of many marginally stable sub-basins within a glass metabasin. In this study, we explore several methods to detect numerically the Gardner transition in a simple structural glass former, the infinite-range Mari-Kurchan model. The transition point is robustly located from three independent approaches: (i) the divergence of the characteristic relaxation time, (ii) the divergence of the caging susceptibility, and (iii) the abnormal tail in the probability distribution function of cage order parameters. We show that the numerical results are fully consistent with the theoretical expectation. The methods we propose may also be generalized to more realistic numerical models as well as to experimental systems.