{"paper":{"title":"Elastic backbone defines a new transition in the percolation model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"Andr\\'e A. Moreira, Cesar I. N. Sampaio Filho, Hans J. Herrmann, Jos\\'e S. Andrade Jr.","submitted_at":"2018-03-21T12:19:49Z","abstract_excerpt":"The elastic backbone is the set of all shortest paths. We found a new phase transition at $p_{eb}$ above the classical percolation threshold at which the elastic backbone becomes dense. At this transition in $2d$ its fractal dimension is $1.750\\pm 0.003$, and one obtains a novel set of critical exponents $\\beta_{eb} = 0.50\\pm 0.02$, $\\gamma_{eb} = 1.97\\pm 0.05$, and $\\nu_{eb} = 2.00\\pm 0.02$ fulfilling consistent critical scaling laws. Interestingly, however, the hyperscaling relation is violated. Using Binder's cumulant, we determine, with high precision, the critical probabilities $p_{eb}$ f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.07876","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"}