Dynamical scaling study for the estimation of dynamical exponent $z$ of three-dimensional XY spin glass model

Abstract

To analyze the $\pm J$ XY spin-glass in three dimensions, we verified a method aimed at obtaining a high-precision dynamical exponent $z$ from the correlation length in the nonequilibrium relaxation process. The obtained $z$ yielded consistent and highly accurate results in previous studies for relatively well-studied models---specifically, the three-dimensional (3D) ferromagnetic Ising model and the 3D $\pm J$ Ising model. Building on these previous studies, we used this method and the dynamical scaling method to analyze the 3D $\pm J$ XY model and obtained highly precise critical temperatures and exponents. The estimated transition temperatures satisfy $T_{\mathrm{SG}}<T_{\mathrm{CG}}$ and are consistent with the spin chirality decoupling picture.