Growth kinetics in a phase field model with continuous symmetry

We discuss the static and kinetic properties of a Ginzburg-Landau spherically symmetric O(N) model recently introduced [U. Marini Bettolo Marconi and A. Crisanti, Phys. Rev. Lett. 75, 2168 (1995)] in order to generalize the so-called phase field model of Langer [Rev. Mod. Phys. 52, 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 diffusive field U follows a conserved dynamics. In the limit N-->infinity 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 wave-vector instability, which is related to the Mullins-Sekerka instability; finally, in the late stage the structure function has a multiscaling behavior, while the domain size grows as t(1/4).