## Abstract

For an Ising model satisfying the Lee-Yang condition, the zeros of the partition function Z and those of the associated functions Z_{A} in the space of imaginary magnetic fields at all lattice sites are determined by a single analytic hypersurface. The sense of motion of the zeros of Z as the interactions are varied can be related to the positions of the zeros of the Z_{A}. Contrary to a plausible conjecture, it is not true that all of the zeros of Z in a uniform field tend towards the point ẑ = 1 in the complex fugacity plane as the temperature is lowered, but it is possible that the first zero (that nearest to ẑ = 1) has a monotone motion. Various simplicity and intertwining properties of the zeros of Z and Z_{A} which generalize earlier results are proved by a new argument which makes direct use of the Lee-Yang property.

Original language | English |
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Pages (from-to) | 2637-2647 |

Number of pages | 11 |

Journal | Journal of Mathematical Physics |

Volume | 24 |

Issue number | 11 |

Publication status | Published - 1982 Dec 1 |

Externally published | Yes |

## ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics