First order phase transitions in unbounded spin systems. II. Completeness of the phase diagram

We continue our analysis of unbounded spin systems with nearest neighbor interactionW and a single spin potentialV which hasN deep and widely separated minima. In this second part we show that all translation invariant phases obeying a certain regularity condition are convex combinations of the stable phases determined in the first part of this paper. For periodic boundary conditions each stable phase contributes with the same weight in the infinite volume limit.