Ground State Entropy and the $q=3$ Potts Antiferromagnet on the Honeycomb Lattice

TL;DR

This paper investigates the $q=3$ Potts antiferromagnet on the honeycomb lattice, demonstrating it remains disordered at all temperatures and calculating its ground state entropy through analytic and simulation methods.

Contribution

It provides the first combined analytic and Monte Carlo analysis showing the disordered nature and specific ground state entropy of the model.

Findings

Model is disordered for all $T \\ge 0$

Ground state entropy is approximately 0.507

Analytic and Monte Carlo methods agree on results

Abstract

We study the $q$-state Potts antiferromagnet with $q=3$ on the honeycomb lattice. Using an analytic argument together with a Monte Carlo simulation, we conclude that this model is disordered for all $T \ge 0$. We also calculate the ground state entropy to be $S_0/k_B = 0.507(10)$ and discuss this result.