Phase ordering of two-dimensional XY systems below the Kosterlitz-Thouless transition temperature

We consider quenches in nonconserved two-dimensional XY systems between any two temperatures below the Kosterlitz-Thouless transition. The evolving systems are defect free at coarse-grained scales, and can be exactly treated. Correlations scale with a characteristic length L(t)∝${\mathit{t}}^{1/2}$ at late times. The autocorrelation decay exponent, λ¯=(${\mathrm{\eta }}_{\mathit{i}}$+${\mathrm{\eta }}_{\mathit{f}}$)/2, depends on both the initial and the final state of the quench through the respective decay exponents of equilibrium correlations, ${\mathit{C}}_{\mathit{eq}}$(r)∼${\mathit{r}}^{\mathrm{-}\mathrm{\eta }}$. We also discuss time-dependent quenches.