Weakly periodic Gibbs measures of the Ising model on the Cayley tree of order five and six

TL;DR

This paper constructs new weakly periodic Gibbs measures for the Ising model on Cayley trees of orders five and six, expanding understanding of non-periodic states in these systems.

Contribution

It introduces novel weakly periodic Gibbs measures associated with specific subgroups, advancing the study of phase structures on Cayley trees.

Findings

New weakly periodic Gibbs measures identified

Measures correspond to subgroups of index two

Results extend understanding of non-periodic phases

Abstract

For Ising model on the Cayley tree of order five and six we present new weakly periodic (non-periodic) Gibbs measures corresponding to normal subgroups of indices two in the group representation of the Cayley tree.