简单的平面图形模型
Planar Graphical Models which are Easy
摘要：
我们描述了一个丰富的家庭的二进制变量统计力学模型在一个给定的平面图，这是等价的高斯格拉斯曼图形模型（自由费米子）定义在同一个图。这种模型的配分函数（加权计数）的计算是容易的（多项式复杂度），因为可简化为对大小等于图中边数的两倍的矩阵的Pfuman的评估。特别是，这种方法涉及Valiant的全息算法，并利用我们以前的工作中讨论的规范变换。
英文摘要：
We describe a rich family of binary variables statistical mechanics models on a given planar graph which are equivalent to Gaussian Grassmann Graphical models (free fermions) defined on the same graph. Calculation of the partition function (weighted counting) for such a model is easy (of polynomial complexity) as reducible to evaluation of a Pfaffian of a matrix of size equal to twice the number of edges in the graph. In particular, this approach touches upon Holographic Algorithms of Valiant and utilizes the Gauge Transformations discussed in our previous works.
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