Abstract
This is the last of a series of papers on the Glauber dynamics of spin systems in with Kac potentials. It deals with phase separation, studying the evolution of an initial state which is a Bernoulli measure with zero average while the temperature of the Glauber dynamics is below the critical value. The state with 0 magnetization is then thermodynamically unstable and we prove that it is so also dynamically. In fact the stable phases, that have magnetization , develop into non-trivial patterns after times proportional to , the range of the Kac interaction. We characterize the typical spin configurations, both during the separation and when this is completed. In particular, we study the magnetization pattern at the boundaries of the clusters and the development of the interfaces.
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