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

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dc.creatorAdda-Bedia, M.
dc.creatorKatzav, E.
dc.creatorVella, D.
dc.date2008-07-28
dc.date2008-09-10
dc.date.accessioned2026-07-07T10:09:46Z
dc.date.available2026-07-07T10:09:46Z
dc.descriptionWe 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)].
dc.descriptionAccepted for publication in J. Chem. Phys. (11 pages, 6 figures)
dc.identifierhttps://arxiv.org/abs/0807.4465
dc.identifierhttp://arxiv.org/abs/0807.4465
dc.identifierJ. Chem. Phys. 129, 144506 (2008)
dc.identifierdoi:10.1063/1.2991338
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/171425
dc.subjectStatistical Mechanics
dc.subjectDisordered Systems and Neural Networks
dc.subjectMaterials Science
dc.subjectSoft Condensed Matter
dc.titleSolution of the Percus-Yevick equation for hard hyperspheres in even dimensions
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