### Abstract

We prove the existence of long-range order at sufficiently low temperatures, including zero temperature, for the three-state Potts antiferromagnet on a class of quasi-transitive plane quadrangulations, including the diced lattice. More precisely, we show the existence of (at least) three infinite-volume Gibbs measures, which exhibit spontaneous magnetization in the sense that vertices in one sublattice have a higher probability to be in one state than in either of the other two states. For the special case of the diced lattice, we give a good rigorous lower bound on this probability, based on computer-assisted calculations that are not available for the other lattices.

Original language | English (US) |
---|---|

Pages (from-to) | 1339-1394 |

Number of pages | 56 |

Journal | Communications in Mathematical Physics |

Volume | 330 |

Issue number | 3 |

DOIs | |

State | Published - 2014 |

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### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

*Communications in Mathematical Physics*,

*330*(3), 1339-1394. https://doi.org/10.1007/s00220-014-2005-1

**Entropy-Driven Phase Transition in Low-Temperature Antiferromagnetic Potts Models.** / Kotecký, Roman; Sokal, Alan D.; Swart, Jan M.

Research output: Contribution to journal › Article

*Communications in Mathematical Physics*, vol. 330, no. 3, pp. 1339-1394. https://doi.org/10.1007/s00220-014-2005-1

}

TY - JOUR

T1 - Entropy-Driven Phase Transition in Low-Temperature Antiferromagnetic Potts Models

AU - Kotecký, Roman

AU - Sokal, Alan D.

AU - Swart, Jan M.

PY - 2014

Y1 - 2014

N2 - We prove the existence of long-range order at sufficiently low temperatures, including zero temperature, for the three-state Potts antiferromagnet on a class of quasi-transitive plane quadrangulations, including the diced lattice. More precisely, we show the existence of (at least) three infinite-volume Gibbs measures, which exhibit spontaneous magnetization in the sense that vertices in one sublattice have a higher probability to be in one state than in either of the other two states. For the special case of the diced lattice, we give a good rigorous lower bound on this probability, based on computer-assisted calculations that are not available for the other lattices.

AB - We prove the existence of long-range order at sufficiently low temperatures, including zero temperature, for the three-state Potts antiferromagnet on a class of quasi-transitive plane quadrangulations, including the diced lattice. More precisely, we show the existence of (at least) three infinite-volume Gibbs measures, which exhibit spontaneous magnetization in the sense that vertices in one sublattice have a higher probability to be in one state than in either of the other two states. For the special case of the diced lattice, we give a good rigorous lower bound on this probability, based on computer-assisted calculations that are not available for the other lattices.

UR - http://www.scopus.com/inward/record.url?scp=84903891784&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84903891784&partnerID=8YFLogxK

U2 - 10.1007/s00220-014-2005-1

DO - 10.1007/s00220-014-2005-1

M3 - Article

AN - SCOPUS:84903891784

VL - 330

SP - 1339

EP - 1394

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 0010-3616

IS - 3

ER -