### Abstract

We study the chromatic polynomial P _{G}(q) for m ≤ n triangular-lattice strips of widths m ≤ 12 _{P}, 9 _{F} (with periodic or free transverse boundary conditions, respectively) and arbitrary lengths n (with free longitudinal boundary conditions). The chromatic polynomial gives the zero-temperature limit of the partition function for the q-state Potts antiferromagnet. We compute the transfer matrix for such strips in the Fortuin-Kasteleyn representation and obtain the corresponding accumulation sets of chromatic zeros in the complex q-plane in the limit n → ∞. We recompute the limiting curve obtained by Baxter in the thermodynamic limit m, n → ∞ and find new interesting features with possible physical consequences. Finally, we analyze the isolated limiting points and their relation with the Beraha numbers.

Original language | English (US) |
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Pages (from-to) | 921-1017 |

Number of pages | 97 |

Journal | Journal of Statistical Physics |

Volume | 112 |

Issue number | 5-6 |

DOIs | |

State | Published - Sep 2003 |

### Keywords

- Antiferromagnetic Potts model
- Beraha numbers
- Beraha-Kahane-Weiss theorem
- Chromatic polynomial
- Chromatic root
- Fortuin-Kasteleyn representation
- Transfer matrix
- Triangular lattice

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics

## Fingerprint Dive into the research topics of 'Transfer Matrices and Partition-Function Zeros for Antiferromagnetic Potts Models. III. Triangular-Lattice Chromatic Polynomial'. Together they form a unique fingerprint.

## Cite this

*Journal of Statistical Physics*,

*112*(5-6), 921-1017. https://doi.org/10.1023/A:1024611424456