On Ground States of Rozikov Model on the Cayley Tree

TL;DR

This paper investigates the ground states of Rozikov's model with finite-range interactions on a Cayley tree, identifying specific periodic configurations that minimize the energy.

Contribution

It provides a detailed description of the periodic ground states for Rozikov's model on a Cayley tree, expanding understanding of its energy-minimizing configurations.

Findings

Identification of a set of periodic ground states

Characterization of ground state configurations

Extension of Rozikov model analysis to finite-range interactions

Abstract

In this paper we consider a model on a Cayley tree which has a finite radius of interactions, the model was first considered by Rozikov. We describe a set of periodic ground states of the model.