Antiferromagnetic Potts Models on the Square Lattice

TL;DR

This paper investigates the antiferromagnetic q-state Potts model on the square lattice for q=3 and q=4, employing advanced Monte Carlo methods and finite-size scaling to analyze phase behavior and correlation lengths.

Contribution

It introduces a new finite-size-scaling extrapolation method and provides detailed analysis of the model's behavior for q=3 and q=4.

Findings

For q=3, correlation length up to ~5000 successfully analyzed.

Data for q=3 are consistent with exponential growth of correlation length.

The q=4 model remains disordered even at zero temperature.

Abstract

We study the antiferromagnetic $q$-state Potts model on the square lattice for $q=3$ and $q=4$, using the Wang-Swendsen-Koteck\'y Monte Carlo algorithm and a new finite-size-scaling extrapolation method. For $q=3$ we obtain good control up to correlation length $\xi \sim 5000$; the data are consistent with $\xi(\beta) = A e^{2\beta} \beta (1 + a_1 e^{-\beta} + \ldots)$ as $\beta\to\infty$. For $q=4$ the model is disordered even at zero temperature.