Translation-invariant Gibbs measures for the fertile HC-models with three states on a Cayley tree

TL;DR

This paper studies translation-invariant Gibbs measures for three-state fertile HC-models on a Cayley tree, providing a detailed description of these measures for models of a specific type and order.

Contribution

It characterizes the translation-invariant Gibbs measures for all four types of three-state fertile HC-models on a Cayley tree of order three, which was previously unexplored.

Findings

Explicit description of Gibbs measures for each model type

Identification of conditions for measure existence

Extension of known models to Cayley trees of order three

Abstract

We consider fertile HC-models with three states on a Cayley tree. It is known that four types of such models exist. For these models we describe the translation-invarinat Gibbs measures on a Cayley tree of order three.