Abstract
A cluster expansion is developed and applied to study the perturbation λ(Δφ)4 of the massless lattice field φ in dimension 3. The method is loosely inspired by the work of Gawedzki and Kupiainen on block spin techniques for the\(\lambda (\mathop \nabla \limits^ \to \phi )^4 \) system. The cluster expansion is given in terms of expansion coefficients for the field as a sum of certain special block spin functions. These functions are chosen with a large number of moments zero, so that the interaction couples spatially separated functions with an interaction falling off as a high inverse power of the separation distance. The present techniques, with some technical development, should work for broad classes of other models, including the lattice dipole gas and the\(\lambda (\mathop \nabla \limits^ \to \phi )^4 \) model. Models λ(,Δ,; φ)2s, α>1/2, are essentially included in the present work.
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Communicated by A. Jaffe
This work was supported in part by the National Science Foundation under Grant No. PHY 79-05688
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Federbush, P.G. A mass zero cluster expansion. Commun.Math. Phys. 81, 327–340 (1981). https://doi.org/10.1007/BF01209071
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DOI: https://doi.org/10.1007/BF01209071