Virial series for fluids of hard hyperspheres in odd dimensions

Abstract

A recently derived method [R. D. Rohrmann and A. Santos, Phys. Rev. E. {\bf 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 $d\ge 5$. Results have been derived up to $d=13$. A confirmation of the alternating character of the series for $d\ge 5$, 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 $d\to \infty$. 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. {\bf 122}, 15 (2006)]

9 pages, 6 figures

References in corpus (5)

• Packing Hyperspheres in High-Dimensional Euclidean Spaces
• Solution of the Percus-Yevick equation for hard discs
• Structure of penetrable-rod fluids: Exact properties and comparison between Monte Carlo simulations and two analytic theories
• Percus-Yevick theory for the structural properties of the seven-dimensional hard-sphere fluid
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Cited by in corpus (6)

• Solution of the Percus-Yevick equation for hard hyperspheres in even dimensions
• Structural and Thermodynamic Properties of Hard-Sphere Fluids
• A branch-point approximant for the equation of state of hard spheres
• Simple equation of state for hard disks on the hyperbolic plane
• Equation of State of Four- and Five-Dimensional Hard-Hypersphere Mixtures
• 1D fluids with repulsive nearest-neighbour interactions: Low-temperature anomalies