Virial series for fluids of hard hyperspheres in odd dimensions

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dc.creatorRohrmann, Rene D.
dc.creatorRobles, Miguel
dc.creatorde Haro, Mariano Lopez
dc.creatorSantos, Andres
dc.date2008-04-29
dc.date.accessioned2026-07-07T09:48:10Z
dc.date.available2026-07-07T09:48:10Z
dc.descriptionA 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 $d \geq 5$. Results have been derived up to $d=13$. A confirmation of the alternating character of the series for $d\geq 5$, 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 $2 η^{1/d}$, where $η$ 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)]
dc.description9 pages, 6 figures
dc.identifierhttps://arxiv.org/abs/0804.4651
dc.identifierhttp://arxiv.org/abs/0804.4651
dc.identifierJ. Chem. Phys. 129, 014510 (2008)
dc.identifierdoi:10.1063/1.2951456
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/164112
dc.subjectSoft Condensed Matter
dc.subjectStatistical Mechanics
dc.subjectChemical Physics
dc.titleVirial series for fluids of hard hyperspheres in odd dimensions
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