Critical Universality of the SU (2) Gauge Glass Model Analyzed by the Dynamical Scaling Method

Abstract

We investigate the critical phenomena of the three-dimensional (3D) $SU(2)$ gauge glass model, which can be regarded as the $O(4)$ spin-glass model with gauge symmetry. Using Monte Carlo simulations and the non-equilibrium relaxation method, we examine the critical behavior along phase boundaries across various degrees of disorder. Consistent with previous studies, we verify that weak disorder is irrelevant to the universality class; the critical behavior of the ferromagnetic-paramagnetic transition remains in the 3D $O(4)$ universality class of the pure ferromagnetic system. Additionally, we demonstrate that the paramagnetic-spin glass transition exhibits universal critical behavior independent of the disorder. Our findings provide valuable insights into the fundamental properties and universality of gauge glass models.