Disorder-induced enhancement and critical scaling of spontaneous magnetization in random-field quantum spin systems

We investigate the effect of a unidirectional quenched random field on the anisotropic quantum spin-1/2 XY model, which magnetizes spontaneously in the absence of the random field. We adopt a mean-field approach for this analysis. In general, the models considered have Ising symmetry, and as such they exhibit ferromagnetic order in two and three dimensions in the presence of not too large disorder. Even in the special case when the model without disorder has U(1) symmetry, a small U(1)-symmetry-breaking random field induces ferromagnetic long-range order in two dimensions. The mean-field approach, consequently, provides a rather good qualitative and even quantitative description when applied not too close to the criticality. We show that spontaneous magnetization persists even in the presence of the random field, but the magnitude of magnetization gets suppressed due to disorder, and the system magnetizes in the directions parallel and transverse to the random field. Our results are obtained via analytical calculations within a perturbative framework and by numerical simulations. Interestingly, we show that it is possible to enhance a component of magnetization in the presence of the disorder field provided that we apply an additional constant field in the XY plane. Moreover, we derive generalized expressions for the critical temperature and the scalings of the magnetization near the critical point for the XY spin system with arbitrary fixed quantum spin angular momentum.