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

Abstract

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.

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

References in corpus (3)

• Exact evolution equation for the effective potential
• Nonperturbative renormalization group approach to frustrated magnets
• Nonperturbative renormalization group approach to the Ising model: a derivative expansion at order ${\partial }^4$