Fundamental measure theory for predicting many-body correlation functions

TL;DR

This paper evaluates various Fundamental Measure Theory formulations for predicting many-body correlation functions in hard-sphere fluids, demonstrating their qualitative accuracy and identifying dominant contributions to four-point correlations, especially in supercooled states.

Contribution

The study compares FMT predictions with Monte Carlo simulations, revealing FMT's strengths and limitations in capturing many-body correlations and simplifying four-point correlation evaluations.

Findings

FMT accurately captures qualitative behavior of three- and four-body structures at low/intermediate wavevectors.

Dominant contributions to four-point structure factors come from direct triplet correlations.

FMT correctly reproduces deviations from the convolution approximation in supercooled liquids.

Abstract

We study many-body correlation functions within various Fundamental Measure Theory (FMT) formulations and compare their predictions to Monte Carlo simulations of hard-sphere fluids. FMT accurately captures the qualitative behavior of three- and four-body structure, particularly at low and intermediate wavevectors. At higher wavevectors, the predictions of FMT vary in quantitative accuracy. We show that the dominant contributions to the four-point structure factor arise from direct triplet correlations, allowing the evaluation of four-point correlations to be greatly simplified. In glass-forming liquids at high volume fractions, FMT correctly reproduces deviations from the convolution approximation, highlighting FMT's ability to capture growing structural multipoint correlations upon supercooling.