Rohrmann René D, Robles Miguel, López de Haro Mariano, Santos Andrés
Observatorio Astronomico, Universidad Nacional de Cordoba, Laprida 854, X5000BGR Cordoba, Argentina.
J Chem Phys. 2008 Jul 7;129(1):014510. doi: 10.1063/1.2951456.
A recently derived method [R. D. Rohrmann and A. Santos, Phys. Rev. E 76, 051202 (2007)] to obtain the exact solution of the Percus-Yevick equation for a fluid of hard spheres in (odd) d dimensions is used to investigate the convergence properties of the resulting virial series. This is done both for the virial and compressibility routes, in which the virial coefficients B(j) are expressed in terms of the solution of a set of (d-1)/2 coupled algebraic equations which become nonlinear for d>/=5. Results have been derived up to d=13. A confirmation of the alternating character of the series for d>/=5, due to the existence of a branch point on the negative real axis, is found and the radius of convergence is explicitly determined for each dimension. The resulting scaled density per dimension 2eta(1/d), where eta is the packing fraction, is wholly consistent with the limiting value of 1 for d-->infinity. Finally, the values for B(j) predicted by the virial and compressibility routes in the Percus-Yevick approximation are compared with the known exact values [N. Clisby and B. M. McCoy, J. Stat. Phys. 122, 15 (2006)].
一种最近推导出来的方法[R. D. 罗尔曼和A. 桑托斯，《物理评论E》76, 051202 (2007)]，用于获得（奇数）d维硬球流体的珀库斯 - 耶维克方程的精确解，被用于研究所得维里级数的收敛性质。这在维里和压缩性途径中都进行了，在这些途径中，维里系数B(j)根据一组(d - 1)/2个耦合代数方程的解来表示，对于d≥5这些方程会变为非线性。结果已推导到d = 13。发现由于在负实轴上存在一个分支点，对于d≥5时级数的交替特征得到了证实，并且明确确定了每个维度的收敛半径。由此得到的每维缩放密度2η(1/d)，其中η是填充率，与d趋于无穷时的极限值1完全一致。最后，将珀库斯 - 耶维克近似中维里和压缩性途径预测的B(j)值与已知的精确值[N. 克利斯比和B. M. 麦科伊，《统计物理杂志》122, 15 (2006)]进行了比较。
