论文标题
一种有效的蒙特卡洛方法，用于制作具有固定连接性的几何图
An Efficient Monte-Carlo Method to Make a Geometric Graph with a Fixed Connectivity
论文作者
论文摘要
我们提出了马尔可夫链蒙特卡洛（MCMC）方法，以制作一个满足以下两个条件的几何图：（i）每个顶点的程度固定为正整数$ k $。 （ii）两个位于$ d $维的高离子晶格上的顶点与边缘连接的可能性与$ d_ {ij}^{ - α} $成正比，其中$ d_ {ij {ij} $是两个顶点和$α$之间的距离。我们介绍了MCMC方法的反向更新方法和基于列表的更新方法。该图通过MCMC方法有效地更新，因为这两个更新方法可以互补。我们还研究了在几何图上定义为测试案例的铁磁学模型。结果，我们已经确认铁磁过渡的性质显着取决于指数$α$。
We present a Markov chain Monte-Carlo (MCMC) method to make a geometric graph which satisfies the following two conditions: (i) The degree of each vertex is fixed to a positive integer $k$. (ii) The probability that two vertices located on a $d$-dimensional hypercubic lattice are connected by an edge is proportional to $d_{ij}^{-α}$, where $d_{ij}$ is the distance between the two vertices and $α$ is a positive exponent. We introduce a reverse update method and a list-based update method for the MCMC method. The graph is updated efficiently by the MCMC method since the two update methods work complementarily. We also investigate a ferromagnetic Ising model defined on the geometric graph as a test case. As a result, we have confirmed that the nature of ferromagnetic transition significantly depends on the exponent $α$.
