### Abstract

We study, using transfer-matrix methods, the partition-function zeros of the square-lattice q-state Potts antiferromagnet at zero temperature (= square-lattice chromatic polynomial) for the boundary conditions that are obtained from an m×n grid with free boundary conditions by adjoining one new vertex adjacent to all the sites in the leftmost column and a second new vertex adjacent to all the sites in the rightmost column. We provide numerical evidence that the partition-function zeros are becoming dense everywhere in the complex q-plane outside the limiting curve B∞(sq) for this model with ordinary (e. g. free or cylindrical) boundary conditions. Despite this, the infinite-volume free energy is perfectly analytic in this region.

Original language | English (US) |
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Pages (from-to) | 1028-1122 |

Number of pages | 95 |

Journal | Journal of Statistical Physics |

Volume | 144 |

Issue number | 5 |

DOIs | |

State | Published - Sep 2011 |

### Keywords

- Beraha-Kahane-Weiss theorem
- Chromatic polynomial
- Chromatic roots
- Extra-vertex boundary conditions
- Planar graph
- Potts model
- Square lattice
- Transfer matrix
- Tutte polynomial

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics

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## Cite this

*Journal of Statistical Physics*,

*144*(5), 1028-1122. https://doi.org/10.1007/s10955-011-0292-x