Hierarchical landscape of hard disk glasses

TL;DR

This study numerically investigates the energy landscape of hard disk glasses near jamming, revealing a hierarchical structure that explains aging and slow dynamics, aligning mean-field predictions with finite-dimensional observations.

Contribution

It demonstrates that the mean-field Gardner phase description applies to finite-dimensional glasses even when the transition is avoided, highlighting a hierarchical landscape structure.

Findings

Aging dynamics emerge as density approaches jamming.

Landscape splits into a hierarchy of minima near jamming.

Mean-field predictions remain relevant for finite-dimensional systems.

Abstract

We numerically analyse the landscape governing the evolution of the vibrational dynamics of hard disk glasses as the density increases towards jamming. We find that the dynamics becomes slow, spatially correlated, and starts to display aging dynamics across an avoided Gardner transition, with a phenomenology that resembles three dimensional observations. We carefully analyse the behaviour of single glass samples, and find that the emergence of aging dynamics is controlled by the apparition of a complex organisation of the landscape that splits into a remarkable hierarchy of minima as jamming is approached. Our results show that the mean-field prediction of a Gardner phase characterized by an ultrametric structure of the landscape provides a useful description of finite dimensional systems, even when the Gardner transition is avoided.