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

We investigate the coarsening kinetics of an XY model defined on a square lattice when the underlying dynamics is governed by energy-conserving Hamiltonian equation of motion. We find that the apparent super-diffusive 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 � (t) with a distinctive exponent of � ≃ 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 �(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.