The Wilson-Polchinski exact renormalization group equation

摘要

The critical exponent eta is not well accounted for in the Polchinski exact formulation of the renormalization group (RG). With a particular emphasis laid on the introduction of the critical exponent eta, I re-establish (after Golner, hep-tti/9801124) the explicit relation between the early Wilson exact RG equation, constructed with the incomplete integration as cutoff procedure, and the formulation with an arbitrary cutoff function proposed later on by Polchinski. I (re)-do the analysis of the Wilson-Polchinski equation expanded up to the next to leading order of the derivative expansion. I finally specify a criterion for choosing the "best" value of eta to this order. This Letter will help in using more systematically the exact RG equation in various studies. (C) 2004, Elsevier B.V. All rights reserved.