Coarsening dynamics of the<i>XY</i>model

Abstract

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 \ensuremath{\rho} should decay with time as \ensuremath{\rho}\ensuremath{\propto}${\mathit{t}}^{\mathrm{\ensuremath{-}}\ensuremath{\nu}}$ with the scaling exponent \ensuremath{\nu}=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 \ensuremath{\nu}=-d(ln\ensuremath{\rho})/d(lnt)=1. Even after the defect density has decayed by three orders of magnitude \ensuremath{\nu}=0.91, which still deviates by 10% from the asymptotic value.