The phase diagram for the bisected-hexagonal-lattice five-state Potts antiferromagnet

TL;DR

This study investigates the phase transitions of the five-state Potts antiferromagnet on the bisected-hexagonal lattice, revealing a weak first-order transition with minimal latent heat, contrasting prior expectations of second-order behavior.

Contribution

The paper provides high-precision Monte Carlo evidence that the transition is first-order, challenging previous suggestions of second-order transition in this system.

Findings

Identified a finite-temperature first-order transition point.

Discovered the coexistence of five phases at low temperature.

Found the latent heat to be two orders of magnitude smaller than typical weak first-order transitions.

Abstract

In this paper we study the phase diagram of the five-state Potts antiferromagnet on the bisected-hexagonal lattice. This question is important since Delfino and Tartaglia recently showed that a second-order transition in a five-state Potts antiferromagnet is allowed, and the bisected-hexagonal lattice had emerged as a candidate for such a transition on numerical grounds. By using high-precision Monte Carlo simulations and two complementary analysis methods, we conclude that there is a finite-temperature first-order transition point. This one separates a paramagnetic high-temperature phase, and a low-temperature phase where five phases coexist. This phase transition is very weak in the sense that its latent heat (per edge) is two orders of magnitude smaller than that of other well-known weak first-order phase transitions.