### Abstract

We prove that the q-state Potts antiferromagnet on a lattice of maximum coordination number r exhibits exponential decay of correlations uniformly at all temperatures (including zero temperature) whenever q>2r. We also prove slightly better bounds for several two-dimensional lattices: square lattice (exponential decay for q≥7), triangular lattice (q≥11), hexagonal lattice (q≥4), and Kagomé lattice (q≥6). The proofs are based on the Dobrushin uniqueness theorem.

Original language | English (US) |
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Pages (from-to) | 551-579 |

Number of pages | 29 |

Journal | Journal of Statistical Physics |

Volume | 86 |

Issue number | 3-4 |

DOIs | |

State | Published - Feb 1997 |

### Keywords

- Antiferromagnetic Potts models
- Dobrushin uniqueness theorem
- Phase transition

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics

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## Cite this

Salas, J., & Sokal, A. D. (1997). Absence of phase transition for antiferromagnetic Potts models via the Dobrushin uniqueness theorem.

*Journal of Statistical Physics*,*86*(3-4), 551-579. https://doi.org/10.1007/BF02199113