GROWTH-KINETICS IN A PHASE FIELD MODEL WITH CONTINUOUS SYMMETRY

We discuss the static and kinetic properties of a Ginzburg-Landau sphe rically symmetric O(N) model recently introduced [U. Marini Bettolo Ma rconi and A. Crisanti, Phys. Rev. Lett. 75, 2168 (1995)] in order to g eneralize the so-called phase field model of Langer [Rev. Mod. Phys. 5 2, 1 (1980); Science 243, 1150 (1989)]. The Hamiltonian contains two O (N) invariant fields phi and U bilinearly coupled. The order parameter field phi evolves according to a nonconserved dynamics, whereas the d iffusive field U follows a conserved dynamics. In the limit N-->infini ty we obtain an exact solution, which displays an interesting kinetic behavior characterized by three different growth regimes. In the early regime the system displays normal scaling and the average domain size grows as t(1/2), in the intermediate regime one observes a finite wav e-vector instability, which is related to the Mullins-Sekerka instabil ity; finally, in the late stage the structure function has a multiscal ing behavior, while the domain size grows as t(1/4).