Ground states for Potts model with a countable set of spin values on a Cayley tree

TL;DR

This paper investigates the ground states of a Potts model with countably infinite spins and competing interactions on a Cayley tree of order three, focusing on periodic configurations.

Contribution

It provides a detailed analysis of periodic ground states for the Potts model with infinite spin values on a Cayley tree, a novel extension of existing models.

Findings

Characterization of periodic ground states for the model

Identification of conditions for stability of ground states

Extension of ground state analysis to countably infinite spin sets

Abstract

We consider Potts model, with competing interactions and countable spin values $\Phi=\{0,1,\dots \}$ on a Cayley tree of order three. We study periodic ground states for this model.