## Abstract

We study the antiferromagnetic q-state Potts model on the square lattice for q = 3 and q = 4, using the Wang-Swendsen-Kotecký (WSK) Monte Carlo algorithm and a powerful finite-size-scaling extrapolation method. For q = 3 we obtain good control up to correlation length ξ ∼ 5000; the data are consistent with ξ(β) = Ae^{2β}β^{p}(1 + a_{1}e^{-β} + ⋯) as β → ∝, with p ≈.1. The staggered susceptibility behaves as χ_{stagg} ∼ ξ^{5/3}. For q = 4 the model is disordered (ξ ≲ 2) even at zero temperature. In appendices we prove a correlation inequality for Potts antiferromagnets on a bipartite lattice, and we prove ergodicity of the WSK algorithm at zero temperature for Potts antiferromagnets on a bipartite lattice.

Original language | English (US) |
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Pages (from-to) | 461-530 |

Number of pages | 70 |

Journal | Journal of Statistical Physics |

Volume | 96 |

Issue number | 3-4 |

DOIs | |

State | Published - Aug 1999 |

## Keywords

- Algorithm
- Antiferromagnet
- Cluster algorithm
- Finite-size scaling
- Monte Carlo
- Phase transition, zero-temperature critical point
- Potts model
- Square lattice
- Swendsen Wang algorithm, Wang Swendsen-Kotecký

## ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics