Effective average action based approach to correlation functions at finite momenta

TL;DR

This paper introduces a new truncation scheme for the effective average action in the nonperturbative renormalization group, enabling accurate analysis of critical phenomena and correlation functions at finite momenta.

Contribution

It develops a natural modification of the derivative expansion that includes local and irreducible correlations to all orders, improving the description of critical regimes and finite momentum correlation functions.

Findings

Accurately describes critical exponents for various N

Provides good momentum dependence of two-point functions

Relatively easy to implement numerically

Abstract

We present a truncation scheme of the effective average action approach of the nonperturbative renormalization group which allows for an accurate description of the critical regime as well as of correlation functions at finite momenta. The truncation is a natural modification of the standard derivative expansion which includes both all local correlations and two-point and four-point irreducible correlations to all orders in the derivatives. We discuss schemes for both the symmetric and the symmetry broken phase of the O(N) model and present results for D=3. All approximations are done directly in the effective average action rather than in the flow equations of irreducible vertices. The approach is numerically relatively easy to implement and yields good results for all N both for the critical exponents as well as for the momentum dependence of the two-point function.