Upper and Lower Bounds for Ground State Entropy of Antiferromagnetic Potts Models

TL;DR

This paper establishes rigorous upper and lower bounds for the ground state entropy of the q-state Potts antiferromagnet on honeycomb and triangular lattices, providing insights into the model's behavior especially for large q.

Contribution

It introduces new, restrictive bounds for the ground state entropy of the Potts antiferromagnet on specific lattices, advancing theoretical understanding.

Findings

Bounds are particularly tight for large q.

Provides a rigorous mathematical framework for entropy estimation.

Enhances understanding of antiferromagnetic Potts models on honeycomb and triangular lattices.

Abstract

We derive rigorous upper and lower bounds for the ground state entropy of the $q$-state Potts antiferromagnet on the honeycomb and triangular lattices. These bounds are quite restrictive, especially for large $q$.