Solution of the Ornstein–Zernike equation in the vicinity of the critical point of a simple fluid

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Abstract
We present a comparison of the results obtained from numerical and analytical solutions of the mean spherical approximation for hard spheres with a Yukawa tail. The emphasis is on the location of the liquid–vapor critical point and the calculation of the associated critical exponents. This comparison allows us to draw some general conclusions concerning the accuracy of numerical solutions of the Ornstein–Zernike equation in the critical region. One important conclusion is that for any closure correctly describing the divergence of the isothermal compressibility along the critical isotherm, extremely accurate numerical work will be required to calculate the value of the exponent delta. We have also compared numerical solutions obtained inside the two phase region with those from the analytical continuation of the analytical solutions into this regime.