Non-Perturbative Renormalization Group for Simple Fluids

TL;DR

This paper introduces a new non-perturbative renormalization group approach for classical simple fluids, extending existing theories and avoiding previous limitations at subcritical temperatures, with rigorous theoretical foundations.

Contribution

It develops a novel non-perturbative RG framework for simple fluids, connecting scalar field theories and improving upon the Hierarchical Reference Theory.

Findings

Establishes a rigorous mapping between three renormalization flows.

Extends Hierarchical Reference Theory without its subcritical temperature limitations.

Aligns with the effective average action approach in liquid state theory.

Abstract

We present a new non perturbative renormalization group for classical simple fluids. The theory is built in the Grand Canonical ensemble and in the framework of two equivalent scalar field theories as well. The exact mapping between the three renormalization flows is established rigorously. In the Grand Canonical ensemble the theory may be seen as an extension of the Hierarchical Reference Theory (L. Reatto and A. Parola, \textit{Adv. Phys.}, \textbf{44}, 211 (1995)) but however does not suffer from its shortcomings at subcritical temperatures. In the framework of a new canonical field theory of liquid state developed in that aim our construction identifies with the effective average action approach developed recently (J. Berges, N. Tetradis, and C. Wetterich, \textit{Phys. Rep.}, \textbf{363} (2002)).