Order-from-disorder and critical scalings of spontaneous magnetization in random-field quantum spin systems

TL;DR

This paper studies how a unidirectional quenched random field affects spontaneous magnetization in the quantum XY model, revealing suppression, possible enhancement with an additional field, and deriving critical scalings.

Contribution

It provides analytical and numerical analysis of magnetization behavior under disorder, including generalized critical temperature and scaling expressions for arbitrary spin quantum numbers.

Findings

Magnetization persists despite disorder but is suppressed in magnitude.

Applying an additional constant field can enhance magnetization components.

Derived generalized critical temperature and magnetization scaling laws.

Abstract

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 mean-field approach to show that spontaneous magnetization persists even in the presence of this 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 by analytical calculations within perturbative framework and by numerical simulations. Interestingly, we show that it is possible to enhance a component of the magnetization in presence of the disorder field provided 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.