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To study the effect of slow heat conduction during phase separation, wediscuss the relaxation properties of an $O(N)$ symmetric model with Phase fieldtype dynamics, where a non conserved order parameter field couples bilinearlyto 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 richdynamical behavior. Finally the connection with the Mullins-Sekerka instabilityis expounded.Comment: 4 pages, 4 figures included, Postscript file packed with uufiles to  appear on Phy. Rev. Let

Diffusion Limited Growth in Systems with Continuous Symmetry