Negative virial coefficients and the dominance of loose packed diagrams for D-dimensional hard spheres

TL;DR

This paper investigates the behavior of virial coefficients for D-dimensional hard spheres, revealing the dominance of loose packed diagrams and implications for the equations of state.

Contribution

It provides new insights into the sign change of virial coefficients and the dominance of loose packed diagrams in high dimensions.

Findings

B_5 is positive across all dimensions

B_6 becomes negative for D >= 6

Loose packed diagrams dominate for large D or k

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.