Non Perturbative Renormalization Group, momentum dependence of $n$-point functions and the transition temperature of the weakly interacting Bose gas

TL;DR

This paper introduces a new approximation scheme for solving Non Perturbative Renormalization Group equations, accurately capturing momentum dependence of $n$-point functions and applying it to compute the transition temperature shift in a weakly interacting Bose gas.

Contribution

The paper develops an iterative extension of the Local Potential Approximation to obtain full momentum dependence within the Non Perturbative Renormalization Group framework.

Findings

The method reproduces perturbative and scaling regimes accurately.

The leading order result agrees with lattice calculations within 25% uncertainty.

Next-to-leading order results differ by about 10% from accepted values.

Abstract

We propose a new approximation scheme to solve the Non Perturbative Renormalization Group equations and obtain the full momentum dependence of $n$-point functions. This scheme involves an iteration procedure built on an extension of the Local Potential Approximation commonly used within the Non Perturbative Renormalization Group. Perturbative and scaling regimes are accurately reproduced. The method is applied to the calculation of the shift $\Delta T_c$ in the transition temperature of the weakly repulsive Bose gas, a quantity which is very sensitive to all momenta intermediate between these two regions. The leading order result is in agreement with lattice calculations, albeit with a theoretical uncertainty of about 25%. The next-to-leading order differs by about 10% from the best accepted result.