Institute of Theoretical Physics, Faculty of Physics, University of Warsaw, Hoża 69, 00-681 Warsaw, Poland.
J Chem Phys. 2011 Aug 28;135(8):084509. doi: 10.1063/1.3622597.
We use an analytic criterion for vanishing of exponential damping of correlations developed previously [J. Piasecki et al., J. Chem. Phys. 133, 164507 (2010)] to determine the threshold volume fractions for structural transitions in hard sphere systems in dimensions D = 3, 4, 5, and 6, proceeding from the Yvon-Born-Green hierarchy and using the Kirkwood superposition approximation. We conclude that the theory does predict phase transitions in qualitative agreement with numerical studies. We also derive, within the superposition approximation, the asymptotic form of the analytic condition for occurrence of a structural transition in the D → ∞ limit.
我们使用先前开发的用于消失指数阻尼相关性的分析判据[J. Piasecki 等人，J. Chem. Phys. 133, 164507 (2010)]来确定维数 D = 3、4、5 和 6 中的硬球系统结构转变的阈值体积分数，从 Yvon-Born-Green 层次结构出发，并使用 Kirkwood 叠加近似。我们得出结论，该理论确实预测了与数值研究定性一致的相变。我们还在叠加近似范围内，推导出 D→∞极限下结构转变出现的分析条件的渐近形式。
