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

Yusuke Terasawa, Yukiyasu Ozeki

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}}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}}

arXiv:2503.06386Mar 9, 20250 citations

Critical dynamics in the two-dimensional XY-model

David Paul Landau, R.W. Gerling

Journal of Magnetism and Magnetic MaterialsFeb 1, 199215 citations

Short-Time Critical Dynamics of the Three-Dimensional Systems with Long-Range Correlated Disorder

V. V. Prudnikov, Pavel Vladimirovich Prudnikov, B. Zheng +2 more

Monte Carlo simulations of the short-time dynamic behavior are reported for three-dimensional Ising and XY models with long-range correlated disorder at criticality, in the case corresponding to linear defects. The static and dynamic critical exponents are determined for systems starting separately from ordered and disordered initial states. The obtained values of the exponents are in good agreement with results of the field-theoretic description of the critical behavior of these models in the two-loop approximation and with our results of Monte Carlo simulations of three-dimensional Ising model in equilibrium state.Monte Carlo simulations of the short-time dynamic behavior are reported for three-dimensional Ising and XY models with long-range correlated disorder at criticality, in the case corresponding to linear defects. The static and dynamic critical exponents are determined for systems starting separately from ordered and disordered initial states. The obtained values of the exponents are in good agreement with results of the field-theoretic description of the critical behavior of these models in the two-loop approximation and with our results of Monte Carlo simulations of three-dimensional Ising model in equilibrium state.

arXiv:0709.0997Progress of Theoretical PhysicsJun 1, 200727 citations

Dynamical scaling study for the estimation of dynamical exponent

z

of three-dimensional XY spin glass model

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}}