Numerical study of spinodal decomposition for Langevin equations

Abstract

We study the time-dependent Ginzburg-Landau model for spinodal decomposition by numerical solution of the associated Langevin equation. The evolution of the system after deep temperature quenches to many different points in the ordered region of the phase diagram has been followed for time scales that are estimated to be equivalent to at least ${10}^4$ and up to more than ${10}^5$ Monte Carlo steps. Analysis of results obtained for block-correlation functions show that the system exhibits scaling behavior and that the average domain size L(t) grows as L(t)∼$t^{1/4}$ in the time region covered by the calculations. We have also studied the quasistatic structure factor C(q,t). The results obtained for this quantity are consistent with those obtained for the block correlations, although, in agreement with other authors, we find that results for C(q,t) alone are not conclusive.