Abstract
It is shown that aD-component Euclidean quantum field, ϕ=(ϕ1,...,ϕD), with λ|ϕ|4+β|ϕ2| interaction, can be obtained as a limit of (ferromagnetic) classical rotator models; this extends a result of Simon and Griffiths from the caseD=1. For these Euclidean field models, it is then shown that a Lee-Yang theorem applies forD=2 or 3 and that Griffiths' second inequality is valid forD=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 forD=2, an interesting relation between the “parallel” and “transverse” two-point correlations is obtained.
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Communicated by A. S. Wightman
Research supported in part by the National Science Foundation under grant NSF MPS 74-04870.
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Dunlop, F., Newman, C.M. Multicomponent field theories and classical rotators. Commun.Math. Phys. 44, 223–235 (1975). https://doi.org/10.1007/BF01609827
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DOI: https://doi.org/10.1007/BF01609827