Abstract
The divergence of the correlation length 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 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.
- Received 26 March 2019
DOI:https://doi.org/10.1103/PhysRevE.101.013306
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