Fundamental measure theory for predicting many-body correlation functions

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 structures, particularly at low and intermediate wave vectors. At higher wave vectors, 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.