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Negative Virial Coefficients and the Dominance of Loose Packed Diagrams for D-Dimensional Hard Spheres

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Abstract

We study the virial coefficients B k of hard spheres in D dimensions by means of Monte-Carlo integration. We find that B 5 is positive in all dimensions but that B 6 is negative for all D≥6. For 7≤k≤17 we compute sets of Ree–Hoover diagrams and find that either for large D or large k the dominant diagrams are “loose packed.” We use these results to study the radius of convergence and the validity of the many approximations used for the equations of state for hard spheres.

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  1. C. N. Yang Institute for Theoretical Physics, State University of New York at Stony Brook, Stony Brook, New York, 11794-384

    N. Clisby & B. M. McCoy

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Clisby, N., McCoy, B.M. Negative Virial Coefficients and the Dominance of Loose Packed Diagrams for D-Dimensional Hard Spheres. Journal of Statistical Physics 114, 1361–1392 (2004). https://doi.org/10.1023/B:JOSS.0000013960.83555.7d

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