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We consider a classical spin model, of two-dimensional spins, with continuoussymmetry, and investigate the effect of a symmetry breaking unidirectionalquenched disorder on the magnetization of the system. We work in the mean fieldregime. We show, by numerical simulations and by perturbative calculations inthe low as well as in the high temperature limits, that although the continuoussymmetry of the magnetization is lost, the system still magnetizes, albeit witha lower value as compared to the case without disorder. The criticaltemperature at which the system starts magnetizing, also decreases with theintroduction of disorder. However, with the introduction of an additionalconstant magnetic field, the component of magnetization in the direction thatis transverse to the disorder field increases with the introduction of thequenched disorder. We discuss the same effects also for three-dimensionalspins.

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