Disorder-Induced Critical Phenomena in Hysteresis: Numerical Scaling in Three and Higher Dimensions

TL;DR

This paper investigates critical phenomena in hysteresis loops using numerical simulations of the random-field Ising model across three to five dimensions, revealing scaling behavior near the disorder-driven transition.

Contribution

It provides detailed numerical analysis of avalanche behavior and critical scaling in higher dimensions, extending understanding of hysteresis phenomena beyond mean-field theory.

Findings

Scaling laws consistent with epsilon expansion near six dimensions

Critical exponents estimated for 3, 4, and 5 dimensions

Large-scale simulations with up to a billion spins

Abstract

We present numerical simulations of avalanches and critical phenomena associated with hysteresis loops, modeled using the zero-temperature random-field Ising model. We study the transition between smooth hysteresis loops and loops with a sharp jump in the magnetization, as the disorder in our model is decreased. In a large region near the critical point, we find scaling and critical phenomena, which are well described by the results of an epsilon expansion about six dimensions. We present the results of simulations in 3, 4, and 5 dimensions, with systems with up to a billion spins (1000^3).