Determining the nonequilibrium criticality of a Gardner transition via a hybrid study of molecular simulations and machine learning

TL;DR

This paper combines molecular simulations and machine learning to identify and analyze the Gardner transition in a 3D hard-sphere glass, providing new insights into non-equilibrium phase transitions.

Contribution

It introduces a hybrid simulation-machine learning method to determine critical exponents and scaling laws for the Gardner transition, a non-equilibrium phase transition.

Findings

Results are consistent with the theoretical prediction of a Gardner transition.

Scaling laws for finite-size and aging effects are established.

Critical exponents are estimated where traditional methods fail.

Abstract

Apparent critical phenomena, typically indicated by growing correlation lengths and dynamical slowing-down, are ubiquitous in non-equilibrium systems such as supercooled liquids, amorphous solids, active matter and spin glasses. It is often challenging to determine if such observations are related to a true second-order phase transition as in the equilibrium case, or simply a crossover, and even more so to measure the associated critical exponents. Here, we show that the simulation results of a hard-sphere glass in three dimensions, are consistent with the recent theoretical prediction of a Gardner transition, a continuous non-equilibrium phase transition. Using a hybrid molecular simulation-machine learning approach, we obtain scaling laws for both finite-size and aging effects, and determine the critical exponents that traditional methods fail to estimate. Our study provides a novel approach that is useful to understand the nature of glass transitions, and can be generalized to analyze other non-equilibrium phase transitions.