On free energies of the Potts model on the Cayley tree

TL;DR

This paper derives explicit formulas for free energies and entropies of the Potts model on the Cayley tree under various boundary conditions, enhancing understanding of phase behaviors in such systems.

Contribution

It provides new explicit expressions for free energies and entropies of the Potts model on the Cayley tree for multiple boundary conditions, including translation-invariant and periodic cases.

Findings

Explicit formulas for free energies under various boundary conditions

Analysis of entropy related to different Gibbs measures

Extension to weakly periodic boundary conditions

Abstract

For the Potts model on the Cayley tree, some explicit formulae of the free energies and entropies (according to vector-valued boundary conditions (BCs)) are obtained. They include translation-invariant, periodic, Dobrushin-like BCs, as well as those corresponding to weakly periodic Gibbs measures.