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

TL;DR

This paper provides an exact analytical characterization of the paramagnetic and ferromagnetic phases of an Ising model with three interactions on a third-order Cayley tree, including critical temperatures, phase counts, and partition functions.

Contribution

It offers the first exact solutions for the phases and critical properties of this specific Ising model on a third-order Cayley tree, extending previous numerical studies.

Findings

Exact critical temperatures and phase curves derived

Number of phases explicitly determined

Partition function computed analytically

Abstract

In this paper we analytically study the recurrence equations of an Ising model with three competing interactions on a Cayley tree of order three. We exactly describe paramagnetic and ferromagnetic phases of the Ising model. We obtain some rigorous results: critical temperatures and curves, number of phases, partition function. Ganikhodjaev et al. [J. Concrete and Applicable Mathematics, 9 (1), 26-34 (2011)] have numerically studied the Ising model on a second-order Cayley tree. We compare the numerical results to exact solutions of mentioned model.