Coarsening Dynamics in a Two-Dimensional XY Model with Hamiltonian Dynamics

We investigate the coarsening dynamics in the two-dimensional Hamiltonian XY model on a square lattice, beginning with a random state with a specified potential energy and zero kinetic energy. Coarsening of the system proceeds via an increase in the kinetic energy and a decrease in the potential energy, with the total energy being conserved. We find that the coarsening dynamics exhibits a consistently superdiffusive growth of a characteristic length scale as L(t) t1/z with 1/z > 1/2 (ranging from 0.54 to 0.57 for typical values of the energy in the coarsening region). Also, the number of point defects (vortices and antivortices) decreases as NV (t) t.V , with V ranging between 1.0 and 1.1. On the other hand, the excess potential energy decays as U t.U , with a typical exponent of U ' 0.88, which shows deviations from the energy-scaling relation. The spin autocorrelation function exhibits a peculiar time dependence with non-power law behavior that can be fitted well by an exponential of logarithmic power in time. We argue that the conservation of the total Josephson (angular) momentum plays a crucial role for these novel features of coarsening in the Hamiltonian XY model. KCI Citation Count: 8