On new weakly periodic Gibbs measures of Ising model on a Cayley tree

TL;DR

This paper investigates the Ising model on a Cayley tree and introduces new weakly periodic Gibbs measures associated with certain subgroup structures, expanding understanding of phase behavior in such models.

Contribution

It presents novel weakly periodic Gibbs measures for the Ising model on a Cayley tree, linked to normal subgroups of index 2, which were not previously identified.

Findings

Discovery of new weakly periodic Gibbs measures.

Connection between subgroup structures and Gibbs measures.

Enhanced understanding of phase transitions in Cayley tree models.

Abstract

We consider the Ising model on a Cayley tree . For the Ising model found new weakly periodic measures corresponding normal subgroups of index 2 of the group representation of the tree Cayley.