Hysteresis and hierarchies: dynamics of disorder-driven first-order phase transformations

TL;DR

This paper investigates the hysteretic behavior and critical phenomena in disorder-driven first-order phase transitions using the zero-temperature random-field Ising model, revealing universal behavior at a critical disorder point.

Contribution

It introduces a detailed analysis of hysteresis, return-point memory, and avalanches at the critical disorder in the RFIM, combining mean-field theory and 3D simulations.

Findings

Identification of a critical disorder value with an infinite avalanche

Universal behavior at the critical point analyzed via mean-field theory

Preliminary 3D simulation results supporting theoretical predictions

Abstract

We use the zero-temperature random-field Ising model to study hysteretic behavior at first-order phase transitions. Sweeping the external field through zero, the model exhibits hysteresis, the return-point memory effect, and avalanche fluctuations. There is a critical value of disorder at which a jump in the magnetization (corresponding to an infinite avalanche) first occurs. We study the universal behavior at this critical point using mean-field theory, and also present preliminary results of numerical simulations in three dimensions.