On some remarks on the Ising model with competing interactions on a Cayley tree

TL;DR

This paper investigates the Ising model with competing interactions on a Cayley tree, focusing on translation-invariant Gibbs measures and free energies to understand phase behavior.

Contribution

It provides new insights into Gibbs measures and free energies for the Ising model with competing interactions on Cayley trees.

Findings

Characterization of translation-invariant Gibbs measures

Analysis of free energy expressions

Insights into phase transitions in the model

Abstract

In the present paper the Ising model with competing binary $J$ and $J_1$ interactions with spin values $\pm 1$, on a Cayley tree is considered. We study translation-invatiant Gibbs measures and corresponding free energies ones.