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 ρt-ν 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.
All Science Journal Classification (ASJC) codes
- Statistical and Nonlinear Physics
- Statistics and Probability
- Condensed Matter Physics