Phase transition in the 3-state Potts antiferromagnet on the diced lattice

TL;DR

This paper proves entropically-driven long-range order in the 3-state Potts antiferromagnet on the diced lattice at low temperatures and uses Monte Carlo simulations to analyze phase transitions, revealing a specific critical point and universality class.

Contribution

It provides a rigorous proof of long-range order at low temperatures and detailed simulation results for phase transitions in the 3-state and 4-state models.

Findings

Long-range order exists at low temperatures in the 3-state model.

The 3-state model undergoes a phase transition at a specific critical point.

The 4-state model remains disordered across all temperatures.

Abstract

We prove that the 3-state Potts antiferromagnet on the diced lattice (dual of the kagome lattice) has entropically-driven long-range order at low temperatures (including zero). We then present Monte Carlo simulations, using a cluster algorithm, of the 3-state and 4-state models. The 3-state model has a phase transition to the high-temperature disordered phase at v = e^J - 1 = -0.860599 +- 0.000004 that appears to be in the universality class of the 3-state Potts ferromagnet. The 4-state model is disordered throughout the physical region, including at zero temperature.