### Abstract

A general formulation is given of Simon's Ising model inequality: {Mathematical expression} where B is any set of spins separating α from γ. We show that 〈σ_{b}σ_{α}〉 can be replaced by 〈σ_{b}σ_{α}〉_{A} where A is the spin system "inside"B containing α. An advantage of this is that a finite algorithm can be given to compute the transition temperature to any desired accuracy. The analogous inequality for plane rotors is shown to hold if a certain conjecture can be proved. This conjecture is indeed verified in the simplest case, and leads to an upper bound on the critical temperature. (The conjecture has been proved in general by Rivasseau. See notes added in proof.)

Original language | English (US) |
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Pages (from-to) | 127-135 |

Number of pages | 9 |

Journal | Communications In Mathematical Physics |

Volume | 77 |

Issue number | 2 |

DOIs | |

State | Published - Oct 1 1980 |

### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics

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## Cite this

Lieb, E. (1980). A refinement of Simon's correlation inequality.

*Communications In Mathematical Physics*,*77*(2), 127-135. https://doi.org/10.1007/BF01982712