Comment on ``Antiferromagnetic Potts Models''

TL;DR

This paper demonstrates that the Wang-Swendsen-Kotecký algorithm fails to explore all configurations at zero temperature for certain antiferromagnetic 3-state Potts models on specific lattices, raising questions about ergodicity in other cases.

Contribution

It provides a specific nonergodicity result for the Wang-Swendsen-Kotecký algorithm in 3-state Potts models on periodic lattices, highlighting limitations of the algorithm at zero temperature.

Findings

Nonergodicity of the algorithm at zero temperature for q=3 on certain lattices

Open questions about ergodicity for q≥4 and other lattice configurations

Implications for simulation accuracy in antiferromagnetic Potts models

Abstract

We show that the Wang-Swendsen-Koteck\'y algorithm for antiferromagnetic $q$-state Potts models is nonergodic at zero temperature for $q=3$ on periodic $3m \times 3n$ lattices where $m,n$ are relatively prime. For $q \ge 4$ and/or other lattice sizes or boundary conditions, the ergodicity at zero temperature is an open question.