Abstract
In the local potential approximation, renormalization group equations reduce to a semilinear parabolic partial differential equation. We derive this equation and show the relation with the hierarchical model. We construct a family of non-trivial fixed points u *2n ,n=2,3,4,..., which have the form ofn-well potentials and exist in the ranges of dimensions 2<d<d n=2+2/(n−1). Asd←d n u *2n tends to zero. For the Wilson fixed pointu*4, we give bounds on critical exponents. In the case of dipole gas in this approximation we show that no non-trivial fixed points exist.
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Communicated by K. Gawedzki
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Felder, G. Renormalization group in the local potential approximation. Commun.Math. Phys. 111, 101–121 (1987). https://doi.org/10.1007/BF01239018
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DOI: https://doi.org/10.1007/BF01239018