Coarsening dynamics of the XY model

It is the conventional wisdom that the correlation length for the XY model with linear damping should asymptotically grow diffusively as the square root of time after a quench into the ordered phase. This implies that the defect density ρ should decay with time as ρ∝${\mathit{t}}^{\mathrm{-}\nu }$ with the scaling exponent ν=1. We present evidence, by numerically integrating the equations of motion for a two-dimensional XY model, for a logarithmic correction to this scaling which makes it difficult to reach the asymptotic regime ν=-d(lnρ)/d(lnt)=1. Even after the defect density has decayed by three orders of magnitude ν=0.91, which still deviates by 10% from the asymptotic value.