Diffusive Domain Coarsening : Early Time Dynamics and Finite-Size Effects

We study diffusive dynamics of phase separation in a binary mixture, following critical quench, both in spatial dimensions $d=2$ and $d=3$. Particular focus in this work is to obtain information about effects of system size and correction to the growth law via appropriate application of finite-size scaling method to the results obtained from Kawasaki exchange Monte Carlo simulation of Ising model. Observations of only weak size effects and very small correction to scaling in the growth law are significant. The methods used in this work and information thus gathered will be of paramount importance in the study of kinetics of phase separation in fluids and other problems of growing length scale. We also provide detailed discussion on standard methods of understanding simulation results which may lead to inappropriate conclusions.