### Abstract

We present exact calculations of the zero-temperature partition function (chromatic polynomial) P for the q-state Potts antiferromagnet on triangular lattice strips of arbitrarily great length L_{x} vertices and of width L_{y} vertices and, in the L_{x}→∞ limit, the exponent of the ground state entropy, W=e^{S}_{0}/k_{B}. The strips considered, with their boundary conditions (BC), are (a) (FBC_{y}, PBC_{x}) = cyclic for L_{y}=3, 4, (b) (FBC_{y}, TPBC_{x}) = Möbius, L_{y}=3, (c) (PBC_{y}, PBC_{x}) = toroidal, L_{y}=3, (d) (PBC_{y}, TPBC_{x}) = Klein bottle, L_{y}=3, (e) (PBC_{y}, FBC_{x}) = cylindrical, L_{y}=5, 6, and (f) (FBC_{y}, FBC_{x}) = free, L_{y}=5, where F, P, and TP denote free, periodic, and twisted periodic. Several interesting features are found, including the presence of terms in P proportional to cos(2πL_{x}/3) for case (c). The continuous locus of points B where W is nonanalytic in the q plane is discussed for each case and a comparative discussion is given of the respective loci B for families with different boundary conditions. Numerical values of W are given for infinite-length strips of various widths and are shown to approach values for the 2D lattice rapidly. A remark is also made concerning a zero-free region for chromatic zeros. Some results are given for strips of other lattices.

Original language | English |
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Pages (from-to) | 124-155 |

Number of pages | 32 |

Journal | Annals of Physics |

Volume | 290 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2001 Jun 15 |

### All Science Journal Classification (ASJC) codes

- Physics and Astronomy(all)

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## Cite this

*Annals of Physics*,

*290*(2), 124-155. https://doi.org/10.1006/aphy.2001.6143