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

TL;DR

This paper derives recurrence equations for an Ising model on a third-order Cayley tree, characterizes its magnetic phases, and compares exact solutions with previous numerical results.

Contribution

It provides a rigorous analysis of phase types and partition functions for the Ising model on a Cayley tree, including exact solutions and their comparison with prior numerical findings.

Findings

Identification of paramagnetic and ferromagnetic phases

Derivation of recurrence equations for the model

Comparison of exact solutions with numerical results

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].