Functional-renormalization-group approach to classical liquids with short-range repulsion: a scheme without repulsive reference system

TL;DR

This paper presents a novel functional renormalization group method for classical liquids with short-range repulsion that avoids the need for a repulsive reference system, improving accuracy in thermodynamic predictions.

Contribution

It introduces a new RG scheme using cavity distribution functions and a variable coupling path, eliminating the reliance on a hard-core reference in classical liquid models.

Findings

Accurately predicts thermodynamic properties across densities

Matches results of integral-equation methods like HNC and PY

Effective even with hierarchical truncation at low densities

Abstract

The renormalization-group approaches for classical liquids in previous works require a repulsive reference such as a hard-core one when applied to systems with short-range repulsion. The need for the reference is circumvented here by using a functional renormalization group approach for integrating the hierarchical flow of correlation functions along a path of variable interatomic coupling. We introduce the cavity distribution functions to avoid the appearance of divergent terms and choose a path to reduce the error caused by the decomposition of higher order correlation functions. We demonstrate using an exactly solvable one-dimensional models that the resulting scheme yields accurate thermodynamic properties and interatomic distribution at various densities when compared to integral-equation methods such as the hypernetted chain and the Percus-Yevick equation, even in the case where our hierarchical equations are truncated with the Kirkwood superposition approximation, which is valid for low-density cases.