A Contour Method on Cayley Trees.

We consider finite-range lattice models on Cayley trees with two basic properties: the existence of only a finite number of ground states and with a Peierls type condition. We define the notion of a contour for the model on the Cayley tree. By a contour argument we show the existence of s different (where s is the number of ground states) Gibbs measures. [ABSTRACT FROM AUTHOR]