### Abstract

We present exact calculations of the partition function of the q-state Potts model for general q and temperature on strips of the square lattice of width L_{y}=3 vertices and arbitrary length L_{x} with periodic longitudinal boundary conditions, of the following types: (i) (FBC_{y}, PBC_{x})= cyclic, (ii) (FBC_{y}, TPBC_{x})= Möbius, (iii) (PBC_{y}, PBC_{x})= toroidal, and (iv) (PBC_{y}, TPBC_{x})= Klein bottle, where FBC and (T)PBC refer to free and (twisted) periodic boundary conditions. Results for the L_{y}=2 torus and Klein bottle strips are also included. In the infinite-length limit the thermodynamic properties are discussed and some general results are given for low-temperature behavior on strips of arbitrarily great width. We determine the submanifold in the C^{2} space of q and temperature where the free energy is singular for these strips. Our calculations are also used to compute certain quantities of graph-theoretic interest.

Original language | English |
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Pages (from-to) | 234-288 |

Number of pages | 55 |

Journal | Physica A: Statistical Mechanics and its Applications |

Volume | 296 |

Issue number | 1-2 |

DOIs | |

Publication status | Published - 2001 Jul 1 |

### All Science Journal Classification (ASJC) codes

- Statistics and Probability
- Condensed Matter Physics