Monte Carlo renormalization-group study of spinodal decomposition: Scaling and growth.

Abstract

The kinetics of domain growth during the late stages of spinodal decomposition is studied by the Monte Carlo renormalization-group technique. A block-spin transformation is applied to the evolving configurations of the two-dimensional kinetic Ising model with conserved order parameter. This acts to renormalize the growing domains, the moving interfaces between them, and the coupled long-range diffusion fields. The growth law for the average size of domains, R(t)\ensuremath{\sim}${t}^{n}$, where t is time, is determined self-consistently by a matching condition. The result for the growth exponent, n=0.338\ifmmode\pm\else\textpm\fi{}0.008, is consistent with the classical result of Lifshitz and Slyozov for Ostwald ripening, namely, n=(1/3. A scaling form for the structure factor is obtained which is invariant under the renormalization-group transformation, to the accuracy of our study. For large wave numbers k, it is found that the scaled form of the structure factor F is in good agreement with Porod's law; i.e., F(kR)\ensuremath{\sim}1/(kR${)}^{d+1}$, in d=2 dimensions.