Abstract
The divergence of the correlation length ζ 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 ζ 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.
| Original language | English |
|---|---|
| Article number | 013306 |
| Journal | Physical Review E |
| Volume | 101 |
| Issue number | 1 |
| DOIs | |
| State | Published - 13 Jan 2020 |
Bibliographical note
Publisher Copyright:© 2020 American Physical Society.
Funding
S.V.B. acknowledges the support by HDTRA1-14-1-0017 and the partial support through the Dr. Bernard W. Gamson Computational Science Center at Yeshiva College. We also acknowledge Robert M. Ziff for helpful comments on the manuscript.
| Funders |
|---|
| Yeshiva University |
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