Ising model on Cayley trees: a new class of Gibbs measures and their comparison with known ones

TL;DR

This paper introduces a broad new class of Gibbs measures for the Ising model on Cayley trees, analyzes their extremality under certain temperatures, and compares them with existing measures.

Contribution

It presents a novel class of Gibbs measures for the Ising model on Cayley trees and compares these with previously known measures.

Findings

New Gibbs measures are extreme under certain temperature conditions.

The paper provides a comprehensive review of known Gibbs measures on trees.

Comparison shows differences and similarities with existing measures.

Abstract

For the Ising model on Cayley trees we give a very wide class of new Gibbs measures. We show that these new measures are extreme under some conditions on the temperature. We give a review of all known Gibbs measures of the Ising model on trees and compare them with our new measures.