Classical spin models with broken symmetry: Random Field Induced Order and Persistence of spontaneous magnetization in presence of a random field

TL;DR

This paper investigates how unidirectional quenched disorder affects magnetization in classical spin models with continuous symmetry, showing that disorder reduces symmetry but can induce magnetization in specific directions, with effects varying by dimension.

Contribution

The study provides analytical and numerical insights into the persistence and behavior of magnetization under symmetry-breaking disorder across different spin models and dimensions.

Findings

Disorder reduces continuous symmetry but allows magnetization in specific directions.

Critical temperature and magnetization are estimated in the presence of disorder.

Disorder effects increase with the dimension of the spin model.

Abstract

We consider classical spin models of two- and three-dimensional spins with continuous symmetry and investigate the effect of a symmetry-breaking unidirectional quenched disorder on the magnetization of the system. We work in the mean-field regime. We show, by perturbative calculations and numerical simulations, that although the continuous symmetry of the magnetization is lost due to disorder, the system still magnetizes in specific directions, albeit with a lower value as compared to the case without disorder. The critical temperature, at which the system starts magnetizing, as well as the magnetization at low and high temperature limits, in presence of disorder, are estimated. Moreover, we treat the SO(n) n-component spin model to obtain the generalized expressions for the near-critical scalings, which suggest that the effect of disorder in magnetization increases with increasing dimension. We also study the behavior of magnetization of the classical XY spin model in the presence of a constant magnetic field, in addition to the quenched disorder. We find that in presence of the uniform magnetic field, disorder may enhance the component of magnetization in the direction that is transverse to the disorder field.