Instanton Analysis of Hysteresis in the Three-Dimensional Random-Field Ising Model

TL;DR

This paper analyzes magnetic hysteresis in the 3D random-field Ising model using instanton techniques to identify disorder configurations that trigger avalanches, providing insights into the critical disorder strength and local two-level systems.

Contribution

It introduces an instanton-based analytical approach to study hysteresis and disorder effects in the 3D random-field Ising model, revealing the mechanisms behind hysteresis smoothness and criticality.

Findings

Estimated critical disorder strength for continuous hysteresis curve

Identified instantons as key configurations triggering avalanches

Described local two-level systems in the ferromagnetic phase

Abstract

We study the magnetic hysteresis in the random field Ising model in 3D. We discuss the disorder dependence of the coercive field H_c, and obtain an analytical description of the smooth part of the hysteresis below and above H_c, by identifying the disorder configurations (instantons) that are the most probable to trigger local avalanches. We estimate the critical disorder strength at which the hysteresis curve becomes continuous. From an instanton analysis at zero field we obtain a description of local two-level systems in the ferromagnetic phase.