Scaling of spatiotemporal correlation in ordering dynamics

The two-time scaling assumption in the system undergoing phase separation is studied numerically. This assumption is written for the order-parameter correlation function as Sₖ(t,t')[Sₖ(t)Sₖ(t')]^-1/2 =V_ψψ(kR(t),t'/t), where k is the wave number, t and t' are times after the quench, R(t) is the length scale, and Sₖ(t) is the same-time correlation function, which scales as Sₖ(t)=R(t)ᵈS ̃ \~{}{}(kR(t)), with d being the spatial dimension. We also examine a power-law expansion of V_ψψ(0,x){∝}(1+{α}/2)x^Δ-{Δ}x^1+α/2 (x{≤}1). Here 0{≤}{Δ}{≤}1+{α}/2, and {α}=d/z-2 for the nonconserved order parameter and {α}=(d+4)/z-2 for the conserved order parameter, where z is the growth-law exponent: R(t)ᶻ{∝}t. For the two-dimensional Ising spin system with Glauber dynamics, we have {α}=-1, and by simulation we found {Δ}{}0.15. We have also done the same analysis for a two-dimensional system with conserved order parameter.