Solution of the Percus-Yevick equation for hard hyperspheres in even dimensions

M. Adda-Bedia; E. Katzav; D. Vella

doi:10.1063/1.2991338

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arXiv · 0807.4465

Solution of the Percus-Yevick equation for hard hyperspheres in even dimensions

M. Adda-Bedia·E. Katzav·D. Vella

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Abstract

We solve the Percus-Yevick equation in even dimensions by reducing it to a set of simple integro-differential equations. This work generalizes an approach we developed previously for hard discs. We numerically obtain both the pair correlation function and the virial coefficients for a fluid of hyper-spheres in dimensions $d=4,6$ and 8, and find good agreement with available exact results and Monte-Carlo simulations. This paper confirms the alternating character of the virial series for $d \ge 6$, and provides the first evidence for an alternating character for $d=4$. Moreover, we show that this sign alternation is due to the existence of a branch point on the negative real axis. It is this branch point that determines the radius of convergence of the virial series, whose value we determine explicitly for $d=4,6,8$. Our results complement, and are consistent with, a recent study in odd dimensions [R.D. Rohrmann et al., J. Chem. Phys. 129, 014510 (2008)].

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M. Adda-Bedia, E. Katzav, D. Vella. 2008-09-10. Solution of the Percus-Yevick equation for hard hyperspheres in even dimensions. https://doi.org/10.1063/1.2991338

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