Preasymptotic multiscaling in the phase-ordering dynamics of the kinetic Ising model

The evolution of the structure factor is studied during the phase-ordering dynamics of the kinetic Ising model with conserved order parameter. A preasymptotic multiscaling regime is found as in the solution of the CahnHilliard-Cook equation, revealing that the late stage of phase-ordering is always approached through a crossover from multiscaling to standard scaling, independently from the nature of the microscopic dynamics. Typeset using REVTEX [email protected] [email protected] 1 Recently we have made an extensive study [1] of the overall time evolution in the phaseordering process with scalar conserved order parameter in the framework of the CahnHilliard-Cook (CHC) equation [2]. Through the careful study of the global evolution of the structure factor from the very beginning of the quench down to the fully developed late stage, we have identified a pattern whereby the very early behavior is followed by an intermediate nonlinear mean-field regime before the asymptotic fully nonlinear regime is attained. Furthermore, the time scales of these regimes have been found to be strongly dependent on (i) the lengthscale considered and (ii) the parameters of the quench such as the amplitude ∆ of the initial fluctuations and the final temperature TF . The concurrence of all these elements gives rise to a rich and interesting variety of behaviors in the preasymptotic phenomenology which can be accounted for in a simple manner on the basis of a model introduced by Bray and Humayun (BH model) [3]. In this paper we make an analogous study of the structure factor in the framework of the kinetic Ising model evolving with Kawasaki dynamics. The main point is that we observe also in this case the existence of an intermediate regime characterized by the mean-field multiscaling behavior, pointing to the generic nature of the above described structure in the overall time evolution. There is abundant experimental and numerical evidence for the universality of the late stage scaling in the phase-ordering process [4] yielding the following form for the structure factor C(~k, t) ∼ L(t)F (kL), (1)