Link between New Versions of the Hierarchical Reference Theory of Liquids and of the Non Perturbative Renormalization Group in Statistical Field Theory

TL;DR

This paper introduces a new version of the Hierarchical Reference Theory of liquids, linking it to a non-perturbative renormalization group framework through parallel formalisms in the grand canonical ensemble and statistical field theory.

Contribution

It establishes a formal connection between the Hierarchical Reference Theory of liquids and non-perturbative renormalization group methods, providing new insights and a unified approach.

Findings

Derived flow equations for Wilsonian and effective average actions

Established a relation between the two functionals

Recovered the standard Hierarchical Reference Theory for liquids

Abstract

I propose a new version of the Hierarchical Reference Theory of liquids. Two formalisms, one in the grand canonical ensemble, the other in the framework of statistical field theory are given in parallel. In the latter the theory is an avatar of a new version of the non perturbative renormalization group (J. Phys. A : Math. Gen. \textbf{42}, 225004 (2009)). The flow of the Wilsonian action as well as that of the effective average action of Wetterich are derived and a simple relation between the two functionals is established. The standard Hierarchical Reference Theory for liquids (\textit{Adv. Phys.} \textbf{44}, 211 (1995)) is recovered for a sharp infra-red cut-off of the propagator