Calculation of the pressure of a hot scalar theory within the Non-Perturbative Renormalization Group

TL;DR

This paper employs a non-perturbative renormalization group method to accurately compute the pressure of a hot scalar field theory across all momentum scales, demonstrating the robustness of the quasiparticle picture and the stability of the approximation scheme.

Contribution

It introduces a non-perturbative RG approach for calculating thermodynamic functions in hot scalar theories, showing improved stability over perturbative methods.

Findings

Small corrections compared to Local Potential Approximation

Robust quasiparticle picture in the system

Stable approximation scheme up to large coupling constants

Abstract

We apply to the calculation of the pressure of a hot scalar field theory a method that has been recently developed to solve the Non-Perturbative Renormalization Group. This method yields an accurate determination of the momentum dependence of n-point functions over the entire momentum range, from the low momentum, possibly critical, region up to the perturbative, high momentum region. It has therefore the potential to account well for the contributions of modes of all wavelengths to the thermodynamical functions, as well as for the effects of the mixing of quasiparticles with multi-particle states. We compare the thermodynamical functions obtained with this method to those of the so-called Local Potential Approximation, and we find extremely small corrections. This result points to the robustness of the quasiparticle picture in this system. It also demonstrates the stability of the overall approximation scheme, and this up to the largest values of the coupling constant that can be used in a scalar theory in 3+1 dimensions. This is in sharp contrast to perturbation theory which shows no sign of convergence, up to the highest orders that have been recently calculated.