Ground states and Gibbs measures of Ising model with competing interactions and an external field on a Cayley tree

Abstract

We consider the Ising model with competing interactions and a nonzero external field on the Cayley tree of order two. We describe ground states and verify the Peierls condition for the model. Using a contour argument we show the existence of two different Gibbs measures.

15 Pages

References in corpus (3)

• A Contour Method on Cayley tree
• Extremal inhomogeneous Gibbs states for SOS-models and finite-spin models on trees
• On $q$- Component Models on Cayley Tree: The General Case