{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/faster-calculation-of-the-percolation","title":"Faster calculation of the percolation correlation length on spatial networks","arxiv_id":"1902.03708","date":"2019-02-11","proceeding":null,"authors":["Michael M. Danziger","Bnaya Gross","Sergey V. Buldyrev"],"abstract":"The divergence of the correlation length $\\xi$ 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 $\\xi$ 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.","url_abs":"http://arxiv.org/abs/1902.03708v2","url_pdf":"http://arxiv.org/pdf/1902.03708v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"faster-calculation-of-the-percolation","repo_url":"https://github.com/mmdanziger/disjointsetsxi","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null},{"paper_slug":"faster-calculation-of-the-percolation","repo_url":"https://github.com/niccolot/Scientific_programming/tree/main/Percolation_random_graphs","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}