B. Yurke et al., COARSENING DYNAMICS OF THE XY MODEL, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 47(3), 1993, pp. 1525-1530
It is the conventional wisdom that the correlation length for the XY m
odel with linear damping should asymptotically grow diffusively as the
square root of time after a quench into the ordered phase. This impli
es that the defect density rho should decay with time as rho is-propor
tional-to t(-nu) with the scaling exponent nu=1. We present evidence,
by numerically integrating the equations of motion for a two-dimension
al XY model, for a logarithmic correction to this scaling which makes
it difficult to reach the asymptotic regime nu=-d(1nrho)/d(1nt)=1. Eve
n after the defect density has decayed by three orders of magnitude nu
=0.91, which still deviates by 10% from the asymptotic value.