Explicit dynamic finite-size scaling in the time-dependent correlation functions for the two-dimensional classical XY model is explored. The dynamic scaling method, proposed by us previously, is utilized for finding the time scaling variables of the model. It shows nontrivial dynamic finite-size scaling behavior near and below TKT for the total spin correlation function. Since the model is critical for all temperatures below TKT, the time scaling exponent is markedly different from that of the three-dimensional classical XY model at short times. There also appears to be another dynamic scaling region with a different time scaling exponent at T⩽TKT for a fairly wide intermediate time interval.Explicit dynamic finite-size scaling in the time-dependent correlation functions for the two-dimensional classical XY model is explored. The dynamic scaling method, proposed by us previously, is utilized for finding the time scaling variables of the model. It shows nontrivial dynamic finite-size scaling behavior near and below TKT for the total spin correlation function. Since the model is critical for all temperatures below TKT, the time scaling exponent is markedly different from that of the three-dimensional classical XY model at short times. There also appears to be another dynamic scaling region with a different time scaling exponent at T⩽TKT for a fairly wide intermediate time interval.

Journal of Applied PhysicsApr 15, 19971 citation

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 of the four-dimensional XY model

Lars Melwyn Jensen

Physica B Condensed MatterJul 1, 20005 citations

Critical dynamics in the two-dimensional XY-model

David Paul Landau, R.W. Gerling

Journal of Magnetism and Magnetic MaterialsFeb 1, 199215 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}}