Virial series for fluids of hard hyperspheres in odd dimensions

ROHRMANN, R. D.; ROBLES, M.; LÓPEZ DE HARO, M.; SANTOS, A.

Journal of Chemical Physics

American Institute of Physics

Lugar: New York; Año: 2008 vol. 129 p. 1 - 8

0021-9606

A recently derived method [R. D. Rohrmann and A. Santos, Phys. Rev. E. 76, 051202 (2007)] to obtain the exact solution of the Percus-Yevick equation for a fluid of hard spheres in (odd) $d$ dimensions is used to investigate the convergence properties of the resulting virial series. This is done both for the virial and compressibility routes, in which the virial coefficients $B_j$ are expressed in terms of the solution of a set of $(d-1)/2$ coupled algebraic equations which become nonlinear for $d geq 5$. Results have been derived up to $d=13$. A confirmation of the alternating character of the series for $dgeq 5$, due to the existence of a branch point on the negative real axis, is found and the radius of convergence is explicitly determined for each dimension. The resulting scaled density per dimension $2 eta^{1/d}$, where $eta$ is the packing fraction, is wholly consistent with the limiting value of 1 for $d o infty$. Finally, the values for $B_j$ predicted by the virial and compressibility routes in the Percus-Yevick approximation are compared with the known exact values [N. Clisby and B. M. McCoy, J. Stat. Phys. 122, 15 (2006)]