Far-from-equilibrium criticality in the Random Field Ising Model with Eshelby Interactions

TL;DR

This paper investigates a zero-temperature random field Ising model with Eshelby interactions, revealing a finite-disorder critical point separating discontinuous and continuous magnetization regimes, with implications for amorphous solids and critical phenomena.

Contribution

It introduces a novel RFIM with Eshelby interactions, identifying a finite-disorder critical point and analyzing its properties in 2D and 3D.

Findings

Discontinuous magnetization with band-like structures at weak disorder

Continuous magnetization with avalanches at strong disorder

Existence of a finite-disorder critical point separating regimes

Abstract

We study a quasi-statically driven random field Ising model (RFIM) at zero temperature with interactions mediated by the long-range anisotropic Eshelby kernel. Analogously to amorphous solids at their yielding transition, and differently from ferromagnetic and dipolar RFIMs, the model shows a discontinuous magnetization jump associated with the appearance of a band-like structure for weak disorder and a continuous magnetization growth, yet punctuated by avalanches, for strong disorder. Through a finite-size scaling analysis in 2 and 3 dimensions we find that the two regimes are separated by a finite-disorder critical point which we characterize. We discuss similarities and differences between the present model and models of sheared amorphous solids.