  We quantify the effect of system size in the kinetics of domain growth in
Ising model with 50:50 composition in two spatial dimensions. Our estimate of
the exponent, $\alpha=0.334\pm0.004$, for the power law growth of linear domain
size, from Monte Carlo simulation using small systems of linear dimensions
L=16, 32, 64, and 128, is in excellent agreement with the prediction of
Lifshitz-Slyozov (LS) theory, $\alpha=1/3$. We find that the LS exponent sets
in very early and continues to be true until average size of domains reaches
three quarters of equilibrium limit.
