Extremality of the unique translation-invariant Gibbs measure for HC models on the Cayley tree of order three

TL;DR

This paper investigates the extremality of the unique translation-invariant Gibbs measure in three-state hard core models on a Cayley tree of order three, focusing on models with known extremal regions.

Contribution

It identifies the extremality regions for the unique Gibbs measure in specific three-state hard core models on a Cayley tree of order three.

Findings

Two types of models have known extremality regions.

The paper advances understanding of Gibbs measure extremality in these models.

Abstract

We consider fertile three-state hard core models with the activity parameter on an order-three Cayley tree. It is known that there exist four types of such models: in two of them the regions of extremality of the unique translation-invariant Gibbs measure were found.