{"paper":{"title":"Correction-to-scaling exponent for percolation and the Fortuin--Kasteleyn Potts model in two dimensions","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"Jes\\'us Salas, Tao Chen, Yihao Xu, Youjin Deng, Zongzheng Zhou","submitted_at":"2024-11-19T16:55:34Z","abstract_excerpt":"The number $n_s$ of clusters (per site) of size $s$, a central quantity in percolation theory, displays at criticality an algebraic scaling behavior of the form $n_s\\simeq s^{-\\tau}\\, A\\, (1+B s^{-\\Omega})$. For the Fortuin--Kasteleyn representation of the $Q$-state Potts model in two dimensions, the Fisher exponent $\\tau$ is known as a function of the real parameter $0\\le Q\\le4$, and, for bond percolation (the $Q\\rightarrow 1$ limit), the correction-to-scaling exponent is derived as $\\Omega=72/91$. We theoretically derive the exact formula for the correction-to-scaling exponent $\\Omega=8/[(2g"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.12646","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2411.12646/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}