Emergence of a random field at the yielding transition of a mean-field Elasto-Plastic model

TL;DR

This paper analyzes the mean-field limit of an elasto-plastic model to understand the emergence of a random field at the yielding transition in amorphous solids, highlighting the analogy with the random-field Ising model.

Contribution

It introduces an analytical characterization of sample-to-sample fluctuations and explores the factors influencing the emergent disorder at the yielding transition.

Findings

Identification of the random field as an emerging disorder

Analytical description of sample-to-sample fluctuations

Insights into the analogy with the random-field Ising model

Abstract

We study the mean-field limit of an elasto-plastic model introduced to describe the yielding transition of athermally and quasi-statically sheared amorphous solids. We focus on the sample-to-sample fluctuations, which we characterize analytically, and investigate in detail the analogy with the athermally driven random-field Ising model. We stress that the random field at the yielding transition is an emerging disorder and we investigate the various factors that determine its strength.