Growth Kinetics in a Phase Field Model with Continuous Symmetry

Details Growth Kinetics in a Phase Field Model with Continuous Symmetry Growth Kinetics in a Phase Field Model with Continuous Symmetry

1996-03-11

arxiv.org/abs/cond-mat/9603074v1

Physics

Condensed Matter

9 pages RevTeX, 9 figures included, files packed with uufiles to appear on Phy. Rev. E

Scientific paper

10.1103/PhysRevE.54.153

We discuss the static and kinetic properties of a Ginzburg-Landau spherically symmetric $O(N)$ model recently introduced (Phys. Rev. Lett. {\bf 75}, 2176, (1995)) in order to generalize the so called Phase field model of Langer. The Hamiltonian contains two $O(N)$ invariant fields $\phi$ and $U$ bilinearly coupled. The order parameter field $\phi$ evolves according to a non conserved dynamics, whereas the diffusive field $U$ follows a conserved dynamics. In the limit $N \to \infty$ 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 wavevector 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 $t^{1/4}$.

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