{"paper":{"title":"One-dimensional long-range percolation: a numerical study","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"A. Trombettoni, G. Gori, M. Michelangeli, N. Defenu","submitted_at":"2016-10-01T22:58:25Z","abstract_excerpt":"In this paper we study bond percolation on a one-dimensional chain with power-law bond probability $C/ r^{1+\\sigma}$, where $r$ is the distance length between distinct sites. We introduce and test an order $N$ Monte Carlo algorithm and we determine as a function of $\\sigma$ the critical value $C_{c}$ at which percolation occurs. The critical exponents in the range $0<\\sigma<1$ are reported and compared with mean-field and $\\varepsilon$-expansion results. Our analysis is in agreement, up to a numerical precision $\\approx 10^{-3}$, with the mean field result for the anomalous dimension $\\eta=2-\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.00200","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"}