论文标题
在D维晶格上相互作用的硬刚性转子的确切结果
Exact Results for Interacting Hard Rigid Rotors on a d-Dimensional Lattice
论文作者
论文摘要
我们研究了一组相同的硬对象的熵，它们的一般形状，每个对象都枢转在晶状体间距A的D维正常晶格的顶点上，但可以具有任意方向。当旋转点不对称地位于对象上时，我们表明存在一系列的晶格间距A，在任何方向上，粒子最多可以与其最多邻居重叠。在此范围内，可以通过有限的负活性在二聚体的基本晶格覆盖物的宏伟分区函数方面准确表示颗粒系统的熵。该范围内的确切熵由第二个病毒系数完全确定。分区函数的计算还显示为具有离散方向的同一模型的计算。我们确定位点方向概率分布函数的确切功能形式。这取决于在二聚体问题中给定活性的二聚体密度，我们通过以数值为单位来求和相应的Mayer系列。这些结果通过数值模拟验证。
We study the entropy of a set of identical hard objects, of general shape, with each object pivoted on the vertices of a d-dimensional regular lattice of lattice spacing a, but can have arbitrary orientations. When the pivoting point is situated asymmetrically on the object, we show that there is a range of lattice spacings a, where in any orientation, a particle can overlap with at most one of its neighbors. In this range, the entropy of the system of particles can be expressed exactly in terms of the grand partition function of coverings of the base lattice by dimers at a finite negative activity. The exact entropy in this range is fully determined by the second virial coefficient. Calculation of the partition function is also shown to be reducible to that of the same model with discretized orientations. We determine the exact functional form of the probability distribution function of orientations at a site. This depends on the density of dimers for the given activity in the dimer problem, that we determine by summing the corresponding Mayer series numerically. These results are verified by numerical simulations.
