Hysteresis Loop Critical Exponents in 6-Epsilon Dimensions

TL;DR

This paper investigates the critical behavior of hysteresis loops in the zero-temperature random-field Ising model near six dimensions, using epsilon-expansion to approximate critical exponents and comparing them with three-dimensional numerical results.

Contribution

It introduces a first-order epsilon-expansion around six dimensions to estimate critical exponents, extending mean-field theory to lower dimensions.

Findings

Epsilon-expansion provides reasonable estimates for 3D critical exponents.

Critical exponents match well with numerical data despite epsilon=3.

Mean-field theory accurately describes behavior above six dimensions.

Abstract

The hysteresis loop in the zero-temperature random-field Ising model exhibits a critical point as the width of the disorder increases. Above six dimensions, the critical exponents of this transition, where the "infinite avalanche" first disappears, are described by mean-field theory. We expand the critical exponents about mean-field theory, in 6-epsilon dimensions, to first order in epsilon. Despite epsilon=3, the values obtained agree reasonably well with the numerical values in three dimensions.