{"paper":{"title":"Statistics of the critical percolation backbone with spatial long-range correlations","license":"","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"A. A. Moreira, A. D. Ara\\'ujo, Jr., J. S. Andrade, R. N. Costa Filho","submitted_at":"2002-10-25T20:09:48Z","abstract_excerpt":"We study the statistics of the backbone cluster between two sites separated by distance $r$ in two-dimensional percolation networks subjected to spatial long-range correlations. We find that the distribution of backbone mass follows the scaling {\\it ansatz}, $P(M_B)\\sim M_B^{-(\\alpha+1)}f(M_B/M_0)$, where $f(x)=(\\alpha+ \\eta x^{\\eta}) \\exp(-x^{\\eta})$ is a cutoff function, and $M_0$ and $\\eta$ are cutoff parameters. Our results from extensive computational simulations indicate that this scaling form is applicable to both correlated and uncorrelated cases. We show that the exponent $\\alpha$ can"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/0210585","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"}