Following the evolution of glassy states under external perturbations: the full replica symmetry breaking solution

TL;DR

This paper develops a full replica symmetry breaking solution to study the evolution of glassy states of Hard Spheres in infinite dimensions under external perturbations like compression and shear, revealing critical behavior and transitions.

Contribution

It provides a detailed theoretical analysis of the Gardner transition in glassy states, including critical exponents, jamming density, and stress-strain behavior, extending previous models with a full RSB approach.

Findings

Metastable states near jamming follow a scaling solution with critical exponents.

Under shear, metastable states exhibit an overshoot in the stress-strain curve.

Critical slowing down characterized by susceptibility and exponents near the Gardner transition.

Abstract

The state-following technique allows the study of metastable glassy states under external perturbations. Here we show how this construction can be used to study the behavior of glassy states of Hard Spheres in infinite dimensions under compression or shear strain. In a preceding work it has been shown that in both cases, when the external perturbation is sufficiently strong, glassy states undergo a second-order transition, called the Gardner transition, whereupon a hierarchical structure of marginal micro-states manifests within the original glass state. The purpose of this work is to study the solution of the state-following construction in this marginal phase. We show that upon compression, close to the jamming transition, the metastable states are described by a scaling solution characterized by a set of non-trivial critical exponents that agree with the results obtained in a preceding work, and we compute the value of the final jamming density for various glassy states. Moreover we show that under the action of the shear strain, beyond the Gardner point, the metastable states can be followed in the marginal phase and we detect an overshoot in the stress-strain curve in agreement with numerical and experimental observations. Finally we further characterize the Gardner transition point by computing both the critical 4-point susceptibility and the exponents that characterize the critical slowing down of the dynamics within a glassy state close to the transition.