Direct correlation functions of the Widom-Rowlinson model

TL;DR

This paper uses Monte Carlo simulations to analyze the direct correlation functions of the Widom-Rowlinson model, comparing results with Percus-Yevick approximation and exploring effects of finite like diameters.

Contribution

It provides the first detailed Monte Carlo analysis of the direct correlation functions in the Widom-Rowlinson model and offers analytical fits for the differences from Percus-Yevick approximation.

Findings

Differences between simulation and Percus-Yevick are well fitted by Gaussians.

Analytical expressions for fit parameters as functions of density are provided.

Simulation data for non-additive hard sphere systems show modifications due to finite like diameters.

Abstract

We calculate, through Monte Carlo numerical simulations, the partial total and direct correlation functions of the three dimensional symmetric Widom-Rowlinson mixture. We find that the differences between the partial direct correlation functions from simulation and from the Percus-Yevick approximation (calculated analytically by Ahn and Lebowitz) are well fitted by Gaussians. We provide an analytical expression for the fit parameters as function of the density. We also present Monte Carlo simulation data for the direct correlation functions of a couple of non additive hard sphere systems to discuss the modification induced by finite like diameters.