# Correlation functions in the Non Perturbative Renormalization Group and field expansion

## TL;DR

This paper analyzes how including all vertices in Non Perturbative Renormalization Group equations affects the calculation of correlation functions, showing rapid convergence at high truncation orders.

## Contribution

It introduces a method that includes all vertices in NPRG equations with approximate momentum dependence, improving accuracy in correlation function calculations.

## Key findings

- Low order truncations significantly underestimate critical exponents.
- High order truncations rapidly converge to accurate results.
- The method is demonstrated using the 3D scalar model at criticality.

## Abstract

The usual procedure of including a finite number of vertices in Non Perturbative Renormalization Group equations in order to obtain $n$-point correlation functions at finite momenta is analyzed. This is done by exploiting a general method recently introduced which includes simultaneously all vertices although approximating their momentum dependence. The study is performed using the self-energy of the tridimensional scalar model at criticality. At least in this example, low order truncations miss quantities as the critical exponent $\eta$ by as much as 60%. However, if one goes to high order truncations the procedure seems to converge rapidly.