Agenda

Résumé : Since about 30 years ago, an approximation scheme called « Derivative Expansion » (DE) has been developed within the framework of the Functional Renormalization Group (which is a modern version of the Wilson Renormalization Group). This approximation scheme does not assume that coupling constants are small and has been extremely successful in the study of various problems in several branches of physics, particularly in Statistical Mechanics. In spite of its various empirical successes, this approximation scheme has been repeatedly questioned, being usually labeled as an « uncontrolled » scheme, lacking of an expansion parameter to ensure that successive corrections tend to be smaller. In this talk, relatively recent advances will be presented showing that the success of DE is not accidental but is associated with a « small parameter » (of the order of 1/4) of a very robust and general nature that suppresses successive orders of such an approximation scheme. Such an advance allows, in particular, to establish a priori error bars estimates of the successive orders of the approximation scheme.