Ninth and Tenth Order Virial Coefficients for Hard Spheres in D Dimensions
Statistical Mechanics
2016-10-06 v1
Abstract
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.
Cite
@article{arxiv.cond-mat/0503525,
title = {Ninth and Tenth Order Virial Coefficients for Hard Spheres in D Dimensions},
author = {N. Clisby and B. M. McCoy},
journal= {arXiv preprint arXiv:cond-mat/0503525},
year = {2016}
}
Comments
33 pages, 12 figures