## Abstract

Using exact results, we determine the complex-temperature phase diagrams of the 2D Ising model on three regular heteropolygonal lattices, (3.6.3.6) (kagome), (3.12^{2}) and (4.8^{2}) (bathroom tile), where the notation denotes the regular n-sided polygons adjacent to each vertex. We also work out the exact complex-temperature singularities of the spontaneous magnetization. A comparison with the properties on the square, triangular, and hexagonal lattices is given. In particular, we find the first case where, even for isotropic spin-spin exchange couplings, the non-trivial non-analyticities of the free energy of the Ising model lie in a two-dimensional, rather than one-dimensional, algebraic variety in the z=e^{-2K} plane.

Original language | English (US) |
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Article number | 014 |

Pages (from-to) | 5235-5256 |

Number of pages | 22 |

Journal | Journal of Physics A: General Physics |

Volume | 28 |

Issue number | 18 |

DOIs | |

State | Published - 1995 |

Externally published | Yes |

## All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Physics and Astronomy(all)
- Mathematical Physics