On the 2-point function of the O(N) model

TL;DR

This paper computes the 2-point function of the 3D O(N) model across all momentum scales using a simple approximation within the Non-Perturbative Renormalization Group framework, showing good agreement with existing results.

Contribution

It introduces a straightforward approximation method to calculate the 2-point function in the O(N) model across all momenta, validated against literature data.

Findings

Results agree well with literature estimates for all N and momenta

The method effectively covers UV to IR regimes

Encourages application to other correlation function calculations

Abstract

The self-energy of the critical 3-dimensional O(N) model is calculated. The analysis is performed in the context of the Non-Perturbative Renormalization Group, by exploiting an approximation which takes into account contributions of an infinite number of vertices. A very simple calculation yields the 2-point function in the whole range of momenta, from the UV Gaussian regime to the scaling one. Results are in good agreement with best estimates in the literature for any value of N in all momenta regimes. This encourages the use of this simple approximation procedure to calculate correlation functions at finite momenta in other physical situations.