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

## TL;DR

This paper investigates the nonperturbative renormalization of the phi^4 model, examining the Wegner-Houghton equation's consistency and its limitations through comparison with perturbative calculations.

## Contribution

It analyzes the validity of the Wegner-Houghton equation in nonperturbative renormalization of the phi^4 model and highlights potential inconsistencies with perturbative results.

## Key findings

- Wegner-Houghton equation is consistent with simple superposition assumptions.
- Expansion coefficients in the renormalized action show inconsistencies with perturbative calculations.
- Raises questions about the exactness of the Wegner-Houghton equation in nonperturbative contexts.

## 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.