### 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) |
---|---|

Pages (from-to) | 223-235 |

Number of pages | 13 |

Journal | Communications in Mathematical Physics |

Volume | 44 |

Issue number | 3 |

DOIs | |

State | Published - Oct 1975 |

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### ASJC Scopus subject areas

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

### Cite this

*Communications in Mathematical Physics*,

*44*(3), 223-235. https://doi.org/10.1007/BF01609827

**Multicomponent field theories and classical rotators.** / Dunlop, François; Newman, Charles M.

Research output: Contribution to journal › Article

*Communications in Mathematical Physics*, vol. 44, no. 3, pp. 223-235. https://doi.org/10.1007/BF01609827

}

TY - JOUR

T1 - Multicomponent field theories and classical rotators

AU - Dunlop, François

AU - Newman, Charles M.

PY - 1975/10

Y1 - 1975/10

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0000217639&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0000217639&partnerID=8YFLogxK

U2 - 10.1007/BF01609827

DO - 10.1007/BF01609827

M3 - Article

VL - 44

SP - 223

EP - 235

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 0010-3616

IS - 3

ER -