### Abstract

It is shown that the spherical model consisting of N spins with nonzero interaction between two spins only has a phase transition in the limit N → ∞. This is a counterexample to a suggestion of Kac which states that an Ising model will have a transition if the corresponding spherical model has a transition. Possible modifications of Kac's conjecture are suggested and discussed.

Original language | English (US) |
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Pages (from-to) | 1403-1406 |

Number of pages | 4 |

Journal | Journal of Mathematical Physics |

Volume | 10 |

Issue number | 8 |

DOIs | |

State | Published - Jan 1 1969 |

### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics

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## Cite this

Lieb, E. H., & Thompson, C. J. (1969). Phase transition in zero dimensions: A remark on the spherical model.

*Journal of Mathematical Physics*,*10*(8), 1403-1406. https://doi.org/10.1063/1.1664980