Effect of Dilute Random Field on Continuous-Symmetry Order Parameter

TL;DR

This study investigates how dilute random fields influence the order parameter in XY and Heisenberg spin systems, revealing glassy behavior, domain formation, and hysteresis scaling, with implications for magnetic and superconducting materials.

Contribution

It introduces a numerical analysis of dilute random field effects on 3D spin systems, linking strong dilute fields to weak continuous fields and explaining complex magnetic phenomena.

Findings

Glassy behavior with initial condition dependence

Formation of ferromagnetic domains inversely proportional to $c_r$

Hysteresis loop area scales as $c_r^2$

Abstract

XY and Heisenberg spins, subjected to strong random fields acting at few points in space with concentration $c_r \ll 1$, are studied numerically on 3d lattices containing over four million sites. Glassy behavior with strong dependence on initial conditions is found. Beginning with a random initial orientation of spins, the system evolves into ferromagnetic domains inversely proportional to $c_r$ in size. The area of the hysteresis loop, $m(H)$, scales as $c_r^2$. These findings are explained by mapping the effect of strong dilute random field onto the effect of weak continuous random field. Our theory applies directly to ferromagnets with magnetic impurities, and is conceptually relevant to strongly pinned vortex lattices in superconductors and pinned charge density waves.