Analytic results for the three- and four-particle correlation functions of the fluid of hard disks

Analytic expressions for the three- and four-particle correlation functions of the hard disk fluid in terms of geometric functionals have been derived using the combined geometric/thermodynamic idea of Boublik [Fluid Phase Equilib. 316, 1 (2012)]. To assess the approximate result, extensive Monte Carlo simulations were performed to obtain the triplet correlation function, g₃, over a wide range of densities. We then focussed on the rolling contact configurations that are required in the second-order thermodynamic perturbation theory of patchy colloid models. The analytic approximation is shown to perform very well, and the simulation data have therefore been parametrized using Boublik's functional form for their subsequent use.