Weakly periodic Gibbs measures Of HC-model for normal divisor of the index four

TL;DR

This paper investigates the existence of weakly periodic Gibbs measures for the HC-model on a Cayley tree, focusing on conditions related to a normal divisor of index four, revealing new non-periodic measure behaviors.

Contribution

It establishes the existence of weakly periodic (non periodic) Gibbs measures for the HC-model on Cayley trees under specific parameter conditions for a normal divisor of index four.

Findings

Existence of weakly periodic Gibbs measures proven

Conditions on parameters for non periodic measures identified

New non periodic measure behaviors characterized

Abstract

In this paper is studied HC-model on a Cayley tree and under some conditions on parameters of the HC-model we prove existence of the weakly periodic (non periodic) Gibbs measures for normal divisor of the index four.