### Abstract

At zero temperature, the 3-state antiferromagnetic Potts model on a square lattice maps exactly onto a point of the 6-vertex model whose long-distance behavior is equivalent to that of a free scalar boson. We point out that at nonzero temperature there are two distinct types of excitation: vortices, which are relevant with renormalization-group eigenvalue 1/2; and non-vortex unsatisfied bonds, which are strictly marginal and serve only to renormalize the stiffness coefficient of the underlying free boson. Together these excitations lead to an unusual form for the corrections to scaling: for example, the correlation length diverges as β ≡ J / kT → ∞ according to ξ ∼ Ae2β(1+bβ^{e-β}+⋯), where b is a nonuniversal constant that may nevertheless be determined independently. A similar result holds for the staggered susceptibility. These results are shown to be consistent with the anomalous behavior found in the Monte Carlo simulations of Ferreira and Sokal.

Original language | English (US) |
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Pages (from-to) | 25-47 |

Number of pages | 23 |

Journal | Journal of Statistical Physics |

Volume | 105 |

Issue number | 1-2 |

DOIs | |

State | Published - Oct 1 2001 |

### Keywords

- Antiferromagnetic Potts model
- Corrections to scaling
- Height representation
- Renormalization group
- Six-vertex model

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics

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## Cite this

*Journal of Statistical Physics*,

*105*(1-2), 25-47. https://doi.org/10.1023/A:1012273825098