### Abstract

In this paper we present exact calculations of the partition function Z of the q-state Potts model and its generalization to real q, for arbitrary temperature on n-vertex strip graphs, of width L_{y} = 2 and arbitrary length, of the triangular lattice with free, cyclic, and Mobius longitudinal boundary conditions. These partition functions are equivalent to Tutte/Whitney polynomials for these graphs. The free energy is calculated exactly for the infinite-length limit of the graphs, and the thermodynamics is discussed. Considering the full generalization to arbitrary complex q and temperature, we determine the singular locus B in the corresponding C^{2} space, arising as the accumulation set of partition function zeros as n→∞. In particular, we study the connection with the T = 0 limit of the Potts antiferromagnet where B reduces to the accumulation set of chromatic zeros. Comparisons are made with our previous exact calculation of Potts model partition functions for the corresponding strips of the square lattice. Our present calculations yield, as special cases, several quantities of graph-theoretic interest.

Original language | English |
---|---|

Pages (from-to) | 189-238 |

Number of pages | 50 |

Journal | Physica A: Statistical Mechanics and its Applications |

Volume | 286 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2000 Oct 15 |

### All Science Journal Classification (ASJC) codes

- Statistics and Probability
- Condensed Matter Physics