Field theory for growth kinetics

Abstract

We present a new field-theory method for growth-kinetics problems which describes the entire time evolution of the system from the early stage after the quench until final equilibrium is attained. The method is developed for a scalar order parameter (conserved or nonconserved) with dynamics of the Langevin type and a systematic low-temperature perturbation scheme is constructed. The main results obtained in lowest order are as follows: (i) a reduced singlet probability distribution which evolves from a Gaussian at early times to a bimodal distribution at late times; (ii) the dynamical separation of two characteristic lengths L(t) and ξ(t) associated, respectively, with the domain size and with the correlation length of fluctuations within a domain; (iii) scaling behavior for the structure factor at long times and a growth law L(t)∼$t^n$ with n=(1/4 for conserved order parameter and n=(1/2 for nonconserved order parameter; and (iv) the realization of the exact equilibrium state, free of spurious Nambu-Goldstone modes, as t→∞. First-order corrections to the structure factor are computed and it is found that they lead to no change in the growth law and to the appropriate first-order temperature corrections in the final equilibrium quantities. Finally the implications of these results for future work are briefly discussed.