Diffusion Limited Growth in Systems with Continuous Symmetry

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.