Yuma Osada | Searcharxiv

arXiv2026

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

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.

cond-mat.dis-nn↗

arXiv2024

Improvement of analysis for relaxation of fluctuations by the use of Gaussian process regression and extrapolation method

The nonequilibrium relaxation (NER) method, which has been used to investigate equilibrium systems via their nonequilibrium behavior, has been widely applied to various models to estimate critical temperatures and critical exponents. Although the estimation of critical temperatures has become more reliable and reproducible, that of critical exponents raises concerns about the method's reliability. Therefore, we propose a more reliable and reproducible approach using Gaussian process regression. In addition, the present approach introduces statistical errors through the bootstrap method by combining them using the extrapolation method. Our estimation for the two-dimensional Ising model yielded $\beta = 0.12504(6)$, $\gamma = 1.7505(10)$, and $\nu = 1.0003(6)$, consistent with the exact values. The value $z = 2.1669(9)$ is reliable because of the high accuracy of these exponents. We also obtained the critical exponents for the three-dimensional Ising model and found that they are close to those reported in a previous study. Thus, for systems undergoing second-order transitions, our approach improves the accuracy, reliability, and reproducibility of the NER analysis. Because the proposed approach requires the relaxation of some observables from Monte Carlo simulations, its simplicity imparts it with significant potential.

cond-mat.stat-mech↗