### Abstract

We present transfer matrices for the zero-temperature partition function of the q-state Potts antiferromagnet (equivalently, the chromatic polynomial) on cyclic and Möbius strips of the square, triangular, and honeycomb lattices of width L_{y} and arbitrarily great length L_{x}. We relate these results to our earlier exact solutions for square-lattice strips with L_{y} = 3, 4, 5, triangular-lattice strips with L_{y} = 2, 3, 4, and honeycomb-lattice strips with L_{y} = 2, 3 and periodic or twisted periodic boundary conditions. We give a general expression for the chromatic polynomial of a Möbius strip of a lattice A and exact results for a subset of honeycomb-lattice transfer matrices, both of which are valid for arbitrary strip width L_{y}. New results are presented for the L_{y} = 5 strip of the triangular lattice and the L_{y} = 4 and L_{y} = 5 strips of the honeycomb lattice. Using these results and taking the infinite-length limit L_{x} → ∞, we determine the continuous accumulation locus of the zeros of the above partition function in the complex q plane, including the maximal real point of nonanalyticity of the degeneracy per site, W as a function of q.

Original language | English |
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Pages (from-to) | 400-450 |

Number of pages | 51 |

Journal | Physica A: Statistical Mechanics and its Applications |

Volume | 346 |

Issue number | 3-4 |

DOIs | |

Publication status | Published - 2005 Feb 15 |

### All Science Journal Classification (ASJC) codes

- Statistics and Probability
- Condensed Matter Physics