Growth Kinetics in a Phase Field Model with Continuous Symmetry

TL;DR

This paper analyzes a generalized phase field model with continuous symmetry, revealing three distinct growth regimes and exact solutions in the large N limit, advancing understanding of phase transition kinetics.

Contribution

It introduces an exactly solvable Ginzburg-Landau model with coupled invariant fields, extending the phase field approach to systems with continuous symmetry.

Findings

Early regime: domain size grows as t^{1/2}

Intermediate regime: finite wavevector instability observed

Late stage: multiscaling behavior with domain size growth as t^{1/4}

Abstract

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 $t^{1/4}$.