Perturbation about the mean field critical point |
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Authors: | Jean Bricmont Jean-Raymond Fontaine Eugene Speer |
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Institution: | (1) Department of Mathematics, Princeton University, 08544 Princeton, NJ, USA;(2) Department of Mathematics, Rutgers University, 08903 New Brunswick, NJ, USA;(3) Present address: Institut de Physique Theorique, Université de Louvain, Belgium |
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Abstract: | We consider two models that are small perturbations of Gaussian or mean field models: the first one is a double well /4 4 — /2 2 perturbation of a massless Gaussian lattice field in the weak coupling limit (![lambda](/content/j533023607767074/xxlarge955.gif) 0, proportional to ). The other consists of a spin 1/2 Ising model with long-range Kac type interactions; the inverse range of the interaction, , is the small parameter. The second model is related to the first one via a sine-Gordon transformation. The lattice
d
has dimensiond 3.In both cases we derive an asymptotic estimate to first order (in or 2) on the location of the critical point. Moreover, we prove bounds on the remainder of an expansion in or around the Gaussian or mean field critical points.The appendix, due to E. Speer, contains an extension of Weinberg's theorem on the divergence of Feynman graphs which is used in the proofs.Supported by NSF Grant # MCS 78-01885Supported by NSF Grant # PHY 78-15920 |
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