Free-energy functional of instantaneous correlation field in liquids: field-theoretic derivation of the closures

TL;DR

This paper develops a field-theoretic approach to derive the free-energy functional of the instantaneous correlation field in liquids, unifying and generalizing existing closure relations in liquid state theory.

Contribution

It introduces a unified field-theoretic derivation of the free-energy functional and closure relations, connecting them to conventional liquid state theories.

Findings

Derivation of the free-energy functional from the grand potential.

Closure relations encompass various known approximations.

Provides a theoretical foundation linking correlation functions and free energy.

Abstract

This paper presents a unified method for formulating a field-theoretic perturbation theory that encompasses the conventional liquid state theory. First, the free-energy functional of instantaneous correlation field is obtained from the functional-integral representation of the grand potential. Next, we demonstrate that the instantaneous free-energy functional yields a closure relation between the correlation functions in the mean-field approximation. Notably, the obtained closure relation covers a variety of approximate closures introduced in the liquid state theory.