Pair Correlation Function Realizability: Lattice Model Implications †
Pair Correlation Function Realizability: Lattice Model Implications †
复制标题
对相关函数的可实现性：格子模型的含义 †
DOI：
10.1021/jp0478155
复制
发表时间：
2004
影响因子：
3.3
通讯作者：
S. Torquato
中科院分区：
文献类型：
--
作者：
F. Stillinger;S. Torquato
尽管它们在实验、模拟和分析理论中有着悠久的历史，但描述多体系统中局部秩序的对相关函数仍然保留着数学上的神秘遗产。一个这样的开放性问题涉及给定候选对相关函数的“可实现性”，即它是否实际上代表了粒子在数密度ρ >0时的某些空间分布的对相关。候选人必须满足的几个必要条件是已知的，包括函数的非负性及其相关的结构因子，以及隐含的局部密度波动的约束。然而，一般条件足以确保可实现性是未知的。为了澄清这种情况，我们已经研究了一个简单的一维晶格模型的可实现性，单网站占用，最近邻排斥。通过对15个或更少的周期边界条件系统的穷举，得到了几个结论。
Despite their long history in experiment, simulation, and analytical theory, pair correlation functions that describe local order in many-body systems still retain a legacy of mathematical mysteries. One such open question concerns “realizability” of a given candidate pair correlation function, namely whether it actually represents the pair correlation for some spatial distribution of particles at number densityρ >0. Several necessary conditions that must be satisfied by the candidate are known, including nonnegativity of the function and its associated structure factor, as well as constraints on implied local density fluctuations. However, general conditions sufficient to ensure realizability are not known. To clarify this situation, we have examined realizability for a simple one-dimensional lattice model, with single-site occupancy, and nearest-neighbor exclusion. By virtue of exhaustive enumeration for systems of 15 or fewer sites subject to periodic boundary conditions, several conclusions have been ...