Coarsening of two-dimensional XY model with Hamiltonian dynamics: logarithmically divergent vortex mobility

Abstract

We investigate the coarsening kinetics of an XY model defined on a square lattice when the underlying dynamics is governed by an energy-conserving Hamiltonian equation of motion. We find that the apparent superdiffusive growth of the length scale can be interpreted as the vortex mobility diverging logarithmically in the size of the vortex–antivortex pair, where the time dependence of the characteristic length scale can be fitted as L(t) ∼ ((t+t0)ln(t+t0))1/2 with a finite offset time t0. This interpretation is based on a simple phenomenological model of vortex–antivortex annihilation to explain the growth of the coarsening length scale L(t). The nonequilibrium spin autocorrelation function A(t) and the growing length scale L(t) are related by A(t) ≃ L−λ(t) with a distinctive exponent of λ ≃ 2.21 (for E = 0.4) possibly reflecting the strong effect of propagating spin-wave modes. We also investigate the nonequilibrium relaxation (NER) of the system under sudden heating of the system from a perfectly ordered state to the regime of quasi-long-range order, which provides a very accurate estimation of the equilibrium correlation exponent η(E) for a given energy E. We find that both the equal-time spatial correlation Cnr(r,t) and the NER autocorrelation Anr(t) exhibit scaling features consistent with the dynamic exponent of znr = 1.