Condensed Matter Physics, 2005, vol. 8, No. 1(41), p. 163-179, English

Title: What can be learnt from the nonperturbative renormalization group?
Authors: B.Delamotte (Laboratoire de Physique Théorique des Liquides, Université Paris VI-Pierre et Marie Curie, 75252 Paris Cedex 05, France) , L.Canet (School of Physics and Astronomy, University of Manchester, Manchester M13 9PL, United Kingdom)

We point out some limits of the perturbative renormalization group used in statistical mechanics both at and out of equilibrium. We argue that the non-perturbative renormalization group formalism is a promising candidate to overcome some of them. We present some results recently obtained in the literature that substantiate our claims. We finally list some open issues for which this formalism could be useful and also review some of its drawbacks.

Key words: renormalization group, nonperturbative field theory, dynamical critical phenomena
PACS: 64.60.Ak, 11.10.Hi, 05.10.Cc

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