New results for the virial coefficients of D-dimensional hard spheres

N. Clisby; B. M. McCoy

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New results for the virial coefficients of D-dimensional hard spheres

N. Clisby·B. M. McCoy

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Abstract

Exact results are given for the fourth virial coefficient of hard spheres in even dimensions up through 12. The fifth and sixth virial coefficients are numerically computed for dimensions 2 through 50 and it is found that the sixth virial coefficient is negative for D >= 6. Numerical studies are made of the contributing Ree Hoover diagrams up to order 17. It is found for D >= 3 that for large order a class of diagrams we call "loose packed" dominates and the rate of growth of these diagrams is used to study bounds on the radius of convergence.

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N. Clisby, B. M. McCoy. 2003-03-20. New results for the virial coefficients of D-dimensional hard spheres. https://arxiv.org/abs/cond-mat/0303101

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