A HC model with countable set of spin values: uncountable set of Gibbs measures

We consider a hard core (HC) model with a countable set \(\mathbb{Z}\) of spin values on the Cayley tree. This model is defined by a countable set of parameters \(\lambda_{i}>0, i \in \mathbb{Z}\setminus\{0\}\). For all possible values of parameters, we give limit points of the dynamical system g...

Full description

Saved in:
Bibliographic Details
Published in:arXiv.org 2022-06
Main Authors: Rozikov, U A, Haydarov, F H
Format: Article
Language:English
Subjects:
Mathematical models
Parameters
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We consider a hard core (HC) model with a countable set \(\mathbb{Z}\) of spin values on the Cayley tree. This model is defined by a countable set of parameters \(\lambda_{i}>0, i \in \mathbb{Z}\setminus\{0\}\). For all possible values of parameters, we give limit points of the dynamical system generated by a function which describes the consistency condition for finite-dimensional measures. Also, we prove that every periodic Gibbs measure for the given model is either translation-invariant or periodic with period two. Moreover, we construct uncountable set of Gibbs measures for this HC model.
ISSN:2331-8422
DOI:10.48550/arxiv.2206.06333