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arXiv:2606.25618

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

Yosei Takada, Yusuke Terasawa, Yuma Osada, Yukiyasu Ozeki

Published Jun 24, 2026• 0 citations
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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.

DOI
10.48550/arxiv.2606.25618

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We investigate the critical phenomena of the three-dimensional (3D) SU(2)SU(2)SU(2) gauge glass model, which can be regarded as the O(4)O(4)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)O(4)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.
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We characterize the dynamic universality classes of a relaxational dynamics under equilibrium conditions at the continuous transitions of three-dimensional (3D) spin systems with Z2{\mathbb{Z}}_{2}Z2​ gauge symmetry. In particular, we consider the pure lattice Z2{\mathbb{Z}}_{2}Z2​ gauge model and the lattice Z2{\mathbb{Z}}_{2}Z2​ gauge XY model, which present various types of transitions: topological transitions without a local order parameter and transitions characterized by both gauge-invariant and non-gauge-invariant XY order parameters. We consider a standard relaxational (locally reversible) Metropolis dynamics and determine the dynamic critical exponent zzz that characterizes the critical slowing down of the dynamics as the continuous transition is approached. At the topological Z2{\mathbb{Z}}_{2}Z2​ gauge transitions we find z=2.55(6)z=2.55(6)z=2.55(6). Therefore, the dynamics is significantly slower than in Ising systems---$z\ensuremath{\approx}2.02$ for the 3D Ising universality class---although 3D Z2{\mathbb{Z}}_{2}Z2​ gauge systems and Ising systems have the same static critical behavior because of duality. As for the nontopological transitions in the 3D Z2{\mathbb{Z}}_{2}Z2​ gauge XY model, we find that their critical dynamics belong to the same dynamic universality class as the relaxational dynamics in ungauged XY systems independently of the gauge-invariant or non-gauge-invariant nature of the order parameter at the transition.
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