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Solution of the PercusYevick equation for hard hyperspheres in even dimensions

Summary: Solution of the Percus­Yevick equation for hard hyperspheres
in even dimensions
M. Adda-Bedia,1
E. Katzav,1,a
and D. Vella1,2
Laboratoire de Physique Statistique, CNRS UMR8550, Ecole Normale Supérieure,
24 rue Lhomond, 75231 Paris Cedex 05, France
ITG, Department of Applied Mathematics and Theoretical Physics, University of Cambridge,
Wilberforce Road, Cambridge CB3 0WA, United Kingdom
Received 28 July 2008; accepted 6 September 2008; published online 14 October 2008
We solve the Percus­Yevick 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


Source: Adda-Bedia, Mokhtar - Laboratoire de Physique Statistique, Département de Physique, École Normale Supérieure


Collections: Physics