Summary: Solution of the Percus­Yevick equation for hard hyperspheres
in even dimensions
M. Adda-Bedia,1
E. Katzav,1,a
and D. Vella1,2
1
Laboratoire de Physique Statistique, CNRS UMR8550, Ecole Normale Supérieure,
24 rue Lhomond, 75231 Paris Cedex 05, France
2
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