GLAUBER EVOLUTION WITH KAC POTENTIALS .3. SPINODAL DECOMPOSITION

This is the last of a series of papers on the Glauber dynamics of spin systems in Z(d) with Kac potentials. It deals with phase separation, studying the evolution of an initial state which is a Bernoulli measur e with zero average while the temperature of the Glauber dynamics is b elow the critical value. The state with 0 magnetization is then thermo dynamically unstable and we prove that it is so also dynamically. In f act the stable phases, that have magnetization +/-m(beta), develop int o non-trivial patterns after times proportional to log gamma(-1), gamm a(-1) the range of the Kac interaction. We characterize the typical sp in configurations, both during the separation and when this is complet ed. In particular, we study the magnetization pattern at the boundarie s of the clusters and the development of the interfaces.