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

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

2003-03-06

arxiv.org/abs/cond-mat/0303101v2

Physics

Condensed Matter

Statistical Mechanics

4 pages, 4 figures, RevTeX, v2: references changed, formatted for PRL

Scientific paper

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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