Costigliola Lorenzo, Schrøder Thomas B, Dyre Jeppe C
Department of Science and Environment, "Glass and Time," IMFUFA, Roskilde University, P.O. Box 260, DK-4000 Roskilde, Denmark.
J Chem Phys. 2016 Jun 21;144(23):231101. doi: 10.1063/1.4954239.
The recent theoretical prediction by Maimbourg and Kurchan [e-print arXiv:1603.05023 (2016)] that for regular pair-potential systems the virial potential-energy correlation coefficient increases towards unity as the dimension d goes to infinity is investigated for the standard 12-6 Lennard-Jones fluid. This is done by computer simulations for d = 2, 3, 4 going from the critical point along the critical isotherm/isochore to higher density/temperature. In both cases the virial potential-energy correlation coefficient increases significantly. For a given density and temperature relative to the critical point, with increasing number of dimension the Lennard-Jones system conforms better to the hidden-scale-invariance property characterized by high virial potential-energy correlations (a property that leads to the existence of isomorphs in the thermodynamic phase diagram, implying that it becomes effectively one-dimensional in regard to structure and dynamics). The present paper also gives the first numerical demonstration of isomorph invariance of structure and dynamics in four dimensions. Our findings emphasize the need for a universally applicable 1/d expansion in liquid-state theory; we conjecture that the systems known to obey hidden scale invariance in three dimensions are those for which the yet-to-be-developed 1/d expansion converges rapidly.
针对标准的12 - 6 Lennard - Jones流体，研究了Maimbourg和Kurchan [电子预印本arXiv:1603.05023 (2016)]最近的理论预测，即对于规则对势系统，随着维度d趋于无穷大，维里势能相关系数趋向于1。这是通过计算机模拟完成的，模拟维度d = 2、3、4，从临界点沿着临界等温线/等容线到更高的密度/温度。在这两种情况下，维里势能相关系数都显著增加。对于相对于临界点给定的密度和温度，随着维度数增加，Lennard - Jones系统更符合以高维里势能相关性为特征的隐藏尺度不变性特性（该特性导致在热力学相图中存在同构体，意味着在结构和动力学方面它有效地变为一维）。本文还首次给出了四维中结构和动力学的同构不变性的数值证明。我们的研究结果强调了液态理论中普遍适用的1/d展开的必要性；我们推测，已知在三维中服从隐藏尺度不变性的系统是那些尚未发展的1/d展开快速收敛的系统。
