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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 systemsize and correction to the growth law via appropriate application offinite-size scaling method to the results obtained from Kawasaki exchange MonteCarlo simulation of Ising model.  Observations of only weak size effects and very small correction to scalingin the growth law are significant. The methods used in this work andinformation thus gathered will be of paramount importance in the study ofkinetics of phase separation in fluids and other problems of growing lengthscale. We also provide detailed discussion on standard methods of understandingsimulation results which may lead to inappropriate conclusions.

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