The divergence of the correlation length ξ at criticality is an important phenomenon of percolation in two-dimensional systems. Substantial speed-ups to the calculation of the percolation threshold and component distribution have been achieved by utilizing disjoint sets, but existing algorithms of this sort cannot measure the correlation length. Here we utilize the parallel axis theorem to track the correlation length as nodes are added to the system, allowing us to utilize disjoint sets to measure ξ for the entire percolation process with arbitrary precision in a single sweep. This algorithm enables direct measurement of the correlation length in lattices as well as spatial network topologies and provides an important tool for understanding critical phenomena in spatial systems.

中文翻译：

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在空间网络上更快地计算渗透相关长度。

临界时相关长度ξ的发散是二维系统中渗流的重要现象。通过使用不相交集，可以大大提高渗滤阈值和组分分布的计算速度，但是现有的此类算法无法测量相关长度。在这里，当节点被添加到系统中时，我们利用平行轴定理来跟踪相关长度，从而使我们能够利用不相交集在一次扫描中以任意精度测量整个渗滤过程的ξ。该算法可以直接测量晶格中的相关长度以及空间网络拓扑，并为理解空间系统中的关键现象提供了重要的工具。