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

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

2005-03-21

arxiv.org/abs/cond-mat/0503525v1

Physics

Condensed Matter

Statistical Mechanics

33 pages, 12 figures

Scientific paper

10.1007/s10955-005-8080-0

We evaluate the virial coefficients B_k for k<=10 for hard spheres in dimensions D=2,...,8. Virial coefficients with k even are found to be negative when D>=5. This provides strong evidence that the leading singularity for the virial series lies away from the positive real axis when D>=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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