Classical Spin Models with Broken Continuous Symmetry: Random Field Induced Order and Persistence of Spontaneous Magnetization

TL;DR

This study investigates how unidirectional quenched disorder affects magnetization in classical spin models with continuous symmetry, showing that disorder reduces magnetization but can induce order in certain directions.

Contribution

It demonstrates through simulations and calculations that quenched disorder influences magnetization and critical temperature, revealing new effects in classical spin models with broken symmetry.

Findings

Disorder lowers the critical temperature for magnetization.

Magnetization persists despite symmetry breaking, with reduced magnitude.

Transverse magnetization component increases with disorder under an external magnetic field.

Abstract

We consider a classical spin model, of two-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 numerical simulations and by perturbative calculations in the low as well as in the high temperature limits, that although the continuous symmetry of the magnetization is lost, the system still magnetizes, albeit with a lower value as compared to the case without disorder. The critical temperature at which the system starts magnetizing, also decreases with the introduction of disorder. However, with the introduction of an additional constant magnetic field, the component of magnetization in the direction that is transverse to the disorder field increases with the introduction of the quenched disorder. We discuss the same effects also for three-dimensional spins.