[Paper Review] Computer simulations of the Gardner transition in structural glasses

Yuliang Jin, Hajime Yoshino|arXiv (Cornell University)|Jun 16, 2022

Material Dynamics and Properties4 citations

TL;DR

This paper uses computer simulations to investigate the Gardner transition in structural glasses, demonstrating that the transition—characterized by full replica symmetry breaking—leads to a hierarchical free-energy landscape and marginal stability. Key findings include protocol-dependent responses, aging dynamics, and irreversible yielding under shear, with strong evidence for the Gardner phase in hard-sphere systems via caging susceptibility, spatial correlations, and ultrametricity.

ABSTRACT

The exact mean-field theory for the simplest glass-forming system - the dense assembly of hard spheres in the large dimensional limit - predicts the existence of a Gardner phase. This transition is characterized by full replica symmetry breaking that implies two fascinating physical consequences: (i) a hierarchical free-energy landscape, and (ii) marginal stability. Here we discuss recent results of numerical simulations to examine these mean-field predictions in physical dimensions.

Motivation & Objective

• To investigate the existence and nature of the Gardner transition in structural glasses using numerical simulations.
• To test mean-field predictions of full replica symmetry breaking (RSB) in physical dimensions, particularly the hierarchical free-energy landscape and marginal stability.
• To explore the connection between the Gardner transition and spin-glass physics through shared RSB universality class and protocol-dependent responses.
• To examine aging effects and non-equilibrium dynamics in the Gardner phase using ZFC/FC-like protocols under shear.
• To assess whether the Gardner transition survives in three dimensions and how it relates to jamming and yielding singularities in hard particles.

Proposed method

• Simulations of dense hard-sphere systems under compression and shear to probe the Gardner transition.
• Use of ZFC/FC-like protocols adapted to shear: measuring response to applied strain after waiting times to study aging.
• Calculation of caging susceptibility and spatial correlations of local caging order parameters to detect the Gardner phase.
• Analysis of stress-strain curves under cyclic shear to identify irreversible behavior and meta-basin destruction.
• Application of the fluctuation-dissipation relation and effective temperature concepts from spin-glass theory to structural glasses.
• Numerical assessment of ultrametricity and power-law scalings in weak forces and interparticle gaps to verify RSB predictions.

Experimental results

Research questions

• RQ1 Does the Gardner transition, predicted by mean-field theory, emerge in three-dimensional structural glasses via computer simulations?
• RQ2 How do protocol-dependent responses—such as those in ZFC/FC-like shear protocols—manifest in the Gardner phase?
• RQ3 To what extent do aging effects and time-dependent responses reflect the hierarchical free-energy landscape and marginal stability?
• RQ4 What is the role of the jamming transition and yielding in the emergence of Gardner physics in hard-sphere systems?
• RQ5 Can experimental signatures of the Gardner phase, such as logarithmic MSD growth and power-law scalings, be reproduced in simulations?

Key findings

• The caging susceptibility grows significantly approaching the Gardner transition, indicating divergent response and criticality.
• Spatial correlations of local caging order parameters become long-ranged in the Gardner phase, signaling heterogeneity in vibrational dynamics.
• Stress-strain curves under cyclic shear show jerky behavior in the Gardner phase due to small avalanches, reflecting marginal stability.
• When the maximum strain exceeds the yield strain, the cycle becomes strongly irreversible, suggesting destruction of the glass meta-basin.
• Numerical evidence supports ultrametricity in jammed hard-sphere packings, confirming the hierarchical free-energy landscape predicted by RSB.
• Simulations show that the Gardner transition is robust in hard-sphere systems but may be interfered with by low-dimensional effects in soft spheres.