## Abstract

I present a new method to exactly compute the partition function of a class of discrete models in arbitrary dimensions. The time for the computation for an n-state model on an L^{d}lattice scales like {Mathematical expression}. I show examples of the use of this method by computing the partition function of the 2D Ising and 3-state Potts models for maximum lattice sizes 10×10 and 8×8, respectively. The critical exponents v and α and the critical temperature one obtains from these are very near the exactly known values. The distribution of zeros of the partition function of the Potts model leads to the conjecture that the ratio of the amplitudes of the specific heat below and above the critical temperature is unity.

Original language | English (US) |
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Pages (from-to) | 55-75 |

Number of pages | 21 |

Journal | Journal of Statistical Physics |

Volume | 60 |

Issue number | 1-2 |

DOIs | |

State | Published - Jul 1990 |

Externally published | Yes |

## All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics

## Keywords

- Potts and Ising models
- exact partition function
- exponents
- scaling
- zeros