Some aspects of the nonperturbative renormalization of the phi^4 model

Details Some aspects of the nonperturbative renormalization of the phi^4 model Some aspects of the nonperturbative renormalization of the phi^4 model

2007-04-02

arxiv.org/abs/0704.0142v2

Int.J.Mod.Phys.B23:5935-5947,2009

Physics

Condensed Matter

Statistical Mechanics

11 pages, no figures. This version is consistent with the accepted (now published) paper.

Scientific paper

10.1142/S0217979209054697

A nonperturbative renormalization of the phi^4 model is considered. First we integrate out only a single pair of conjugated modes with wave vectors +/- q. Then we are looking for the RG equation which would describe the transformation of the Hamiltonian under the integration over a shell Lambda - d Lambda < k < Lambda, where d Lambda -> 0. We show that the known Wegner--Houghton equation is consistent with the assumption of a simple superposition of the integration results for +/- q. The renormalized action can be expanded in powers of the phi^4 coupling constant u in the high temperature phase at u -> 0. We compare the expansion coefficients with those exactly calculated by the diagrammatic perturbative method, and find some inconsistency. It causes a question in which sense the Wegner-Houghton equation is really exact.

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