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Ninth and Tenth Order Virial Coefficients for Hard Spheres in D Dimensions

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Abstract

We evaluate the virial coefficients Bk for \(k\leq 10\) for hard spheres in dimensions \(D=2,\cdots,8.\) Virial coefficients with k even are found to be negative when \(D\geq 5. \) This provides strong evidence that the leading singularity for the virial series lies away from the positive real axis when \(D\geq 5\). Further analysis provides evidence that negative virial coefficients will be seen for some k > 10 for D = 4, and there is a distinct possibility that negative virial coefficients will also eventually occur for D = 3.

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  1. ARC Centre of Excellence for Mathematics and Statistics of Complex Systems, The University of Melbourne, 139 Barry Street, Parkville Victoria, 3010, Australia

    Nathan Clisby

  2. C. N. Yang Institute for Theoretical Physics, Stony Brook University, Stony Brook, NY, 11794-3840, U.S.A.

    Barry M. McCoy

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Clisby, N., McCoy, B.M. Ninth and Tenth Order Virial Coefficients for Hard Spheres in D Dimensions. J Stat Phys 122, 15–57 (2006). https://doi.org/10.1007/s10955-005-8080-0

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