Multicomponent field theories and classical rotators |
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Authors: | François Dunlop Charles M. Newman |
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Affiliation: | (1) Inst. des Hautes Études Scientifiques, F-91 Bures-sur-Yvette, France;(2) Dept. of Mathematics, Indiana University, 47401 Bloomington, Indiana, USA |
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Abstract: | It is shown that aD-component Euclidean quantum field, =(1,...,D), with ||4+|2| 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.Research supported in part by the National Science Foundation under grant NSF MPS 74-04870. |
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