## Abstract

It is shown that a D-component Euclidean quantum field, φ{symbol}=(φ{symbol}^{1},...,φ{symbol}^{D}), with λ|φ{symbol}|^{4}+β|φ{symbol}^{2}| interaction, can be obtained as a limit of (ferromagnetic) classical rotator models; this extends a result of Simon and Griffiths from the case D=1. For these Euclidean field models, it is then shown that a Lee-Yang theorem applies for D=2 or 3 and that Griffiths' second inequality is valid for D=2; a complete proof is included of a Lee-Yang theorem for plane rotator and classical Heisenberg models. As an application of Griffiths' second inequality for D=2, an interesting relation between the "parallel" and "transverse" two-point correlations is obtained.

Original language | English (US) |
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Pages (from-to) | 223-235 |

Number of pages | 13 |

Journal | Communications In Mathematical Physics |

Volume | 44 |

Issue number | 3 |

DOIs | |

State | Published - Oct 1975 |

## ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics