Non-perturbative renormalization group preserving full-momentum dependence: implementation and quantitative evaluation

TL;DR

This paper details the implementation of the BMW nonperturbative renormalization group scheme, enabling full momentum dependence calculations of correlation functions with high accuracy, validated on scalar O(N) theories.

Contribution

It introduces a detailed implementation of the BMW scheme for full-momentum correlation functions and compares it with other methods, demonstrating its effectiveness.

Findings

Accurate computation of critical exponents and two-point functions.

Excellent agreement with existing results across momentum ranges.

Quantitative evaluation of the universal structure factor in high-temperature phase.

Abstract

We present in detail the implementation of the Blaizot-M\'endez-Wschebor (BMW) approximation scheme of the nonperturbative renormalization group, which allows for the computation of the full momentum dependence of correlation functions. We discuss its signification and its relation with other schemes, in particular the derivative expansion. Quantitative results are presented for the testground of scalar O(N) theories. Besides critical exponents which are zero-momentum quantities, we compute in three dimensions in the whole momentum range the two-point function at criticality and, in the high temperature phase, the universal structure factor. In all cases, we find very good agreement with the best existing results.