A Contour Method on Cayley tree

Abstract

We consider a finite range lattice models on Cayley tree with two basic properties: the existence of only a finite number of ground states and with Peierls type condition. We define 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.

12 pages

References in corpus (2)

• Partition function zeros at first-order phase transitions: Pirogov-Sinai theory
• An example of one-dimensional phase transition

Cited by in corpus (1)

• On Ground States of Rozikov Model on the Cayley Tree