Recent developments of the Hierarchical Reference Theory of Fluids and its relation to the Renormalization Group

TL;DR

This paper reviews the Hierarchical Reference Theory (HRT) of fluids, highlighting its foundations, critical properties, and its close relationship with non-perturbative renormalization group methods, including recent generalizations to soft matter and quantum systems.

Contribution

It provides a comprehensive overview of HRT, including both sharp and smooth cut-off formulations, and discusses its recent extensions and connections to renormalization group techniques.

Findings

HRT effectively describes phase transitions in classical and quantum fluids.

The theory's critical properties and behavior at first-order transitions are summarized.

Recent generalizations extend HRT to soft matter and quantum many-body systems.

Abstract

The Hierarchical Reference Theory (HRT) of fluids is a general framework for the description of phase transitions in microscopic models of classical and quantum statistical physics. The foundations of HRT are briefly reviewed in a self-consistent formulation which includes both the original sharp cut-off procedure and the smooth cut-off implementation, which has been recently investigated. The critical properties of HRT are summarized, together with the behavior of the theory at first order phase transitions. However, the emphasis of this presentation is on the close relationship between HRT and non perturbative renormalization group methods, as well as on recent generalizations of HRT to microscopic models of interest in soft matter and quantum many body physics.