Ising Model on the Cayley Tree of Third Order with Inhomogeneous Interactions.

In this paper we investigate the problem of phase transition for Ising model on a semi-infinite Cayley tree of third order with inhomogeneous left, middle and right parameters describing the strength of the interactions between left, middle and right nearest-neighbors respectively. We produce a recurrent equation that describes a limit behavior of the sequence conditional Gibbs measures and prove that if at least two of the parameters are positive one can reach phase transition. [ABSTRACT FROM AUTHOR]