Two-dimensional Potts antiferromagnets with a phase transition at arbitrarily large q

TL;DR

This paper demonstrates that certain two-dimensional lattice models of the q-state Potts antiferromagnet exhibit finite-temperature phase transitions even at arbitrarily large q, challenging previous expectations.

Contribution

It provides the first rigorous proof of phase transitions at large q for specific 2D lattices and combines analytical and numerical methods to support the findings.

Findings

Existence of phase transitions at large q on specific lattices

Rigorous proof using Peierls argument

Numerical data supporting theoretical results

Abstract

We exhibit infinite families of two-dimensional lattices (some of which are triangulations or quadrangulations of the plane) on which the q-state Potts antiferromagnet has a finite-temperature phase transition at arbitrarily large values of q. This unexpected result is proven rigorously by using a Peierls argument to measure the entropic advantage of sublattice long-range order. Additional numerical data are obtained using transfer matrices, Monte Carlo simulation, and a high-precision graph-theoretic method.