Allegra Nicolas, Fortin Jean-Yves
Institut Jean Lamour, CNRS/UMR 7198, Groupe de Physique Statistique, Université de Lorraine, BP 70239, F-54506 Vandœuvre-lès-Nancy Cedex, France.
Phys Rev E Stat Nonlin Soft Matter Phys. 2014 Jun;89(6):062107. doi: 10.1103/PhysRevE.89.062107. Epub 2014 Jun 4.
We present an application of the Grassmann algebra to the problem of the monomer-dimer statistics on a two-dimensional square lattice. The exact partition function, or total number of possible configurations, of a system of dimers with a finite set of n monomers at fixed positions can be expressed via a quadratic fermionic theory. We give an answer in terms of a product of two pfaffians and the solution is closely related to the Kasteleyn result of the pure dimer problem. Correlation functions are in agreement with previous results, both for monomers on the boundary, where a simple exact expression is available in the discrete and continuous case, and in the bulk where the expression is evaluated numerically.
我们展示了格拉斯曼代数在二维方格上单体 - 二聚体统计问题中的应用。对于固定位置有有限个(n)个单体的二聚体系统，其精确的配分函数或可能构型的总数可通过二次费米子理论来表示。我们给出了一个用两个普法夫式乘积表示的答案，并且该解与纯二聚体问题的卡斯泰莱因结果密切相关。关联函数与先前的结果一致，对于边界上的单体，在离散和连续情况下都有一个简单的精确表达式，而在体相中则通过数值计算来评估表达式。
