Diffusion Limited Growth in Systems with Continuous Symmetry

TL;DR

This paper investigates the complex growth behaviors in an $O(N)$ symmetric model with phase field dynamics, revealing three growth regimes and connecting to Mullins-Sekerka instability, with an exact solution in the large N limit.

Contribution

It provides an exact solution for the relaxation properties of a coupled $O(N)$ model with phase field dynamics in the large N limit, highlighting diverse growth regimes and their relation to instability phenomena.

Findings

Identified three distinct growth regimes.

Derived an exact solution in the large N limit.

Connected growth behavior to Mullins-Sekerka instability.

Abstract

To study the effect of slow heat conduction during phase separation, we discuss the relaxation properties of an $O(N)$ symmetric model with Phase field type dynamics, where a non conserved order parameter field couples bilinearly to a diffusive field. In the limit $N\to\infty$ we obtain an exact solution. The analysis reveals three different types of growth regimes and a very rich dynamical behavior. Finally the connection with the Mullins-Sekerka instability is expounded.