Kinetics of ordering for correlated initial conditions

Nonequilibrium domain growth in a system with a nonconserved order parameter is considered for power-law correlated initial conditions, [φ(r)φ(0)]∼${\mathit{r}}^{\mathrm{-}\left(\mathit{d}\mathrm{-}\mathrm{\sigma }\right)}$, appropriate to, e.g., a quench to the ordered phase from the critical point (σ=2-η). The long-range correlations are shown to be relevant (in the renormalization-group sense), and lead to a new scaling function for the structure factor, provided that σ exceeds a critical value. In this regime (which includes σ=2-η) the autocorrelation function A(t)==[φ(r,t)φ(r,0)] has the asymptotic behavior A(t)∼${\mathit{t}}^{\mathrm{-}\left(\mathit{d}\mathrm{-}\mathrm{\sigma }\right)/4\mathrm{}}$.