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Particles and scaling for lattice fields and Ising models
Authors:James Glimm  Arthur Jaffe
Institution:(1) Rockefeller University, 10021 New York, N. Y., USA;(2) Harvard University, 02138 Cambrige, Mass., USA
Abstract:The conjectured inequality gamma(6)lE0 leads to the existence of phiv d 4 fields and the scaling (continuum) limit ford-dimensional Ising models. Assuming gamma(6)lE0 and Lorentz covariance of this construction, we show that fordgE6 these phiv d 4 fields are free fields unless the field strength renormalizationZ –1 diverges. Let lambda be the bare charge and epsi the lattice spacing. Under the same assumptions (gamma(6)lE0, Lorentz covariance anddgE6) we show that if lambdaepsi4–d is bounded as epsirarr0, thenZ –1 is bounded and the limit field is free.Supported in part by the National Science Foundation under Grant MPS 74-13252Supported in part by the National Science Foundation under Grant MPS 75-21212
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