### 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) |
---|---|

Pages (from-to) | 551-579 |

Number of pages | 29 |

Journal | Journal of Statistical Physics |

Volume | 86 |

Issue number | 3-4 |

State | Published - Feb 1997 |

### Fingerprint

### Keywords

- Antiferromagnetic Potts models
- Dobrushin uniqueness theorem
- Phase transition

### ASJC Scopus subject areas

- Mathematical Physics
- Physics and Astronomy(all)
- Statistical and Nonlinear Physics

### Cite this

*Journal of Statistical Physics*,

*86*(3-4), 551-579.

**Absence of phase transition for antiferromagnetic Potts models via the Dobrushin uniqueness theorem.** / Salas, Jeśus; Sokal, Alan D.

Research output: Contribution to journal › Article

*Journal of Statistical Physics*, vol. 86, no. 3-4, pp. 551-579.

}

TY - JOUR

T1 - Absence of phase transition for antiferromagnetic Potts models via the Dobrushin uniqueness theorem

AU - Salas, Jeśus

AU - Sokal, Alan D.

PY - 1997/2

Y1 - 1997/2

N2 - 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.

AB - 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.

KW - Antiferromagnetic Potts models

KW - Dobrushin uniqueness theorem

KW - Phase transition

UR - http://www.scopus.com/inward/record.url?scp=0038967484&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0038967484&partnerID=8YFLogxK

M3 - Article

VL - 86

SP - 551

EP - 579

JO - Journal of Statistical Physics

JF - Journal of Statistical Physics

SN - 0022-4715

IS - 3-4

ER -