{"paper":{"title":"Explosive Percolation is Continuous, but with Unusual Finite Size Behavior","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.dis-nn","authors_text":"Claire Christensen, Golnoosh Bizhani, Maya Paczuski, Peter Grassberger, Seung-Woo Son","submitted_at":"2011-03-18T23:25:39Z","abstract_excerpt":"We study four Achlioptas type processes with \"explosive\" percolation transitions. All transitions are clearly continuous, but their finite size scaling functions are not entire holomorphic. The distributions of the order parameter, the relative size $s_{\\rm max}/N$ of the largest cluster, are double-humped. But -- in contrast to first order phase transitions -- the distance between the two peaks decreases with system size $N$ as $N^{-\\eta}$ with $\\eta > 0$. We find different positive values of $\\beta$ (defined via $< s_{\\rm max}/N > \\sim (p-p_c)^\\beta$ for infinite systems) for each model, sho"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.3728","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":""},"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"}