Determination of paramagnetic and ferromagnetic phases of an Ising model on a third-order Cayley tree

Abstract

In this present paper, the recurrence equations of an Ising model with three coupling constants on a third-order Cayley tree are obtained. Paramagnetic and ferromagnetic phases associated with the Ising model are characterized. Types of phases and partition functions corresponding to the model are rigorously studied. Exact solutions of the mentioned model are compared with the numerical results given in Ganikhodjaev et al. [J. Concr. Appl. Math., 2011, 9, No. 1, 26-34].