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

M. Adda-Bedia*, E. Katzav, D. Vella

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

22 Scopus citations


We solve the Percus-Yevick equation in even dimensions by reducing it to a set of simple integrodifferential equations. This work generalizes an approach we developed previously for hard disks. We numerically obtain both the pair correlation function and the virial coefficients for a fluid of hyperspheres in dimensions d = 4, 6, and 8, and find good agreement with the available exact results and Monte Carlo simulations. This paper confirms the alternating character of the virial series for d≥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, J. Chem. Phys. 129, 014510 (2008)].

Original languageAmerican English
Article number144506
JournalJournal of Chemical Physics
Issue number14
StatePublished - 2008
Externally publishedYes

Bibliographical note

Funding Information:
We would like to thank Professor Whitlock and Professor Bishop for sharing their data with us, and Professor Santos for his useful comments. This work was supported by the Royal Commission for the Exhibition of 1851 (D.V.). Laboratoire de Physique Statistique is associated with Universities Paris VI and Paris VII.


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