Critical Hysteresis in Random Field XY and Heisenberg Models

TL;DR

This paper investigates zero-temperature hysteresis in random-field XY and Heisenberg models, revealing how disorder type influences critical hysteresis and loop shapes, with exact mean field solutions and clarification of previous discrepancies.

Contribution

It provides exact mean field solutions for hysteresis in these models and clarifies differences with earlier renormalization group studies.

Findings

Disorder form significantly affects critical hysteresis

Exact solutions in mean field limit are obtained

Resolves discrepancies with previous RG studies

Abstract

We study zero-temperature hysteresis in random-field XY and Heisenberg models in the zero-frequency limit of a cyclic driving field. We consider three distributions of the random field and present exact solutions in the mean field limit. The results show a strong effect of the form of disorder on critical hysteresis as well as the shape of hysteresis loops. A discrepancy with an earlier study based on the renormalization group is resolved.