Revisiting the local potential approximation of the exact renormalization group equation |
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Authors: | C. Bervillier |
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Affiliation: | Laboratoire de Mathématiques et Physique Théorique, UMR 7350 (CNRS), Fédération Denis Poisson, Université François Rabelais, Parc de Grandmont, 37200 Tours, France |
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Abstract: | The conventional absence of field renormalization in the local potential approximation (LPA) — implying a zero value of the critical exponent η — is shown to be incompatible with the logic of the derivative expansion of the exact renormalization group (RG) equation. We present a LPA with η≠0 that strictly does not make reference to any momentum dependence. Emphasis is made on the perfect breaking of the reparametrization invariance in that pure LPA (absence of any vestige of invariance) which is compatible with the observation of a progressive smooth restoration of that invariance on implementing the two first orders of the derivative expansion whereas the conventional requirement (η=0 in the LPA) precluded that observation. |
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Keywords: | Local potential approximation Derivative expansion Exact renormalization group equation Reparametrization invariance Anomalous dimension |
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