Journal of Statistical Physics

, Volume 122, Issue 1, pp 15–57 | Cite as

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

  • Nathan Clisby
  • Barry M. McCoy


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.

Key Words

Hard spheres virial expansion 


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© Springer Science + Business Media, Inc. 2006

Authors and Affiliations

  1. 1.ARC Centre of Excellence for Mathematics and Statistics of Complex SystemsThe University of MelbourneParkville VictoriaAustralia
  2. 2.C. N. Yang Institute for Theoretical PhysicsStony Brook UniversityStony BrookU.S.A.

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