## Abstract

We present exact solutions for the zero-temperature partition function (chromatic polynomial P) and the ground state degeneracy per site W (= exponent of the ground-state entropy) for the q-state Potts antiferromagnet on strips of the square lattice of width L_{y} vertices and arbitrarily great length L_{x} vertices. The specific solutions are for (a) L_{y} = 4, (FBC_{y}, PBC_{x}) (cyclic); (b) L_{y} = 4, (FBC_{y}, TPBC_{x}) (Mobius); (c) L_{y} = 5,6, (PBC_{y}, FBC_{x}) (cylindrical); and (d) L_{y} = 5, (FBC_{y}, FBC_{x}) (open), where FBC, PBC, and TPBC denote free, periodic, and twisted periodic boundary conditions, respectively. In the L_{x}→∞ limit of each strip we discuss the analytic structure of W in the complex q plane. The respective W functions are evaluated numerically for various values of q. Several inferences are presented for the chromatic polynomials and analytic structure of W for lattice strips with arbitrarily great L_{y}. The absence of a nonpathological L_{x}→∞ limit for real nonintegral q in the interval 0<q<3 (0<q<4) for strips of the square (triangular) lattice is discussed.

Original language | English |
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Pages (from-to) | 402-430 |

Number of pages | 29 |

Journal | Physica A: Statistical Mechanics and its Applications |

Volume | 290 |

Issue number | 3-4 |

DOIs | |

Publication status | Published - 2001 Feb 15 |

## All Science Journal Classification (ASJC) codes

- Statistics and Probability
- Condensed Matter Physics