Solutions of renormalization group flow equations with full momentum dependence

TL;DR

This paper introduces a new approximation scheme for non-perturbative renormalization group equations, enabling full momentum dependence of correlation functions, and demonstrates its effectiveness by computing two-point functions in O(N) theories at criticality.

Contribution

It presents a novel approximation method that allows solving renormalization group flow equations with full momentum dependence, improving accuracy for critical phenomena.

Findings

Accurate two-point functions for O(N) theories at criticality.

Effective computation of universal and non-universal quantities.

Method achieves good results with modest computational effort.

Abstract

We demonstrate the power of a recently-proposed approximation scheme for the non-perturbative renormalization group that gives access to correlation functions over their full momentum range. We solve numerically the leading-order flow equations obtained within this scheme, and compute the two-point functions of the O(N) theories at criticality, in two and three dimensions. Excellent results are obtained for both universal and non-universal quantities at modest numerical cost.