Dynamic critical exponent of two-, three-, and four-dimensional XY models with relaxational and resistively shunted junction dynamics

Abstract

The dynamic critical exponent $z$ is determined numerically for the $d$-dimensional XY model ($d=2,3$, and 4) subject to relaxational dynamics and resistively shunted junction dynamics. We investigate both the equilibrium fluctuation and the relaxation behavior from nonequilibrium towards equilibrium, using the finite-size scaling method. The resulting values of $z$ are shown to depend on the boundary conditions used, the periodic boundary condition, and fluctuating twist boundary condition (FTBC), which implies that the different treatments of the boundary in some cases give rise to different critical dynamics. It is also found that the equilibrium scaling and the approach to equilibrium scaling for the the same boundary condition do not always give the same value of $z$. The FTBC in conjunction with the finite-size scaling of the linear resistance for both type of dynamics yields values of $z$ consistent with expectations for superfluids and superconductors: $z=2$, 3/2, and 2 for $d=2$, 3, and 4, respectively.

arXiv comment21 pages, 16 figures, final version

References in corpus (19)

• Dynamic Monte Carlo Measurement of Critical Exponents
• Breakdown of Scaling in the Nonequilibrium Critical Dynamics of the Two-Dimensional XY Model
• 3D-XY critical fluctuations of the thermal expansivity in detwinned YBa2Cu3O7-d single crystals near optimal doping
• Dynamic transition in vortex flow in strongly disordered Josephson junction arrays and superconducting thin films
• Dynamic scaling for 2D superconductors, Josephson junction arrays and superfluids
• 3D XY and lowest Landau level fluctuations in deoxygenated YBCO thin films
• Current-voltage scaling of chiral and gauge-glass models of two-dimensional superconductors
• Spin dynamics simulation of the three-dimensional XY model: Structure factor and transport properties
• Dynamical universality classes of the superconducting phase transition
• Numerical Study of Spin and Chiral Order in a Two-Dimensional XY Spin Glass
• Monte Carlo calculation of the current-voltage characteristics of a two dimensional lattice Coulomb gas
• 1/ω-flux-noise and dynamical critical properties of two-dimensional XY-models
• Monte Carlo calculation of the linear resistance of a three dimensional lattice Superconductor model in the London limit
• Numerical Study of Order in a Gauge Glass Model
• Langevin Simulations of Two Dimensional Vortex Fluctuations: Anomalous Dynamics and a New $IV$-exponent
• Dynamics of d-wave Vortices: Angle-Dependent Nonlinear Hall Effect
• Critical Relaxation and Critical Exponents
• Critical scaling of the a.c. conductivity for a superconductor above Tc
• Dynamic critical behaviors of three-dimensional XY models related to superconductors/superfluids

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• Corrections to Scaling for the Two-dimensional Dynamic XY Model
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