{"paper":{"title":"Ising model with spins S=1/2 and 1 on directed and undirected Erd\\\"os-R\\'enyi random graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.dis-nn","authors_text":"F.W.S. Lima, M.A.Sumour","submitted_at":"2011-09-11T13:20:41Z","abstract_excerpt":"Using Monte Carlo simulations we study the Ising model with spin S=1/2 and 1 on {\\it directed} and {\\it undirected} Erd\\\"os-R\\'enyi (ER) random graphs, with $z$ neighbors for each spin. In the case with spin S=1/2, the {\\it undirected} and {\\it directed} ER graphs present a spontaneous magnetization in the universality class of mean field theory, where in both {\\it directed} and {\\it undirected} ER graphs the model presents a spontaneous magnetization at $p = z/N$ ($z=2, 3, ...,N$), but no spontaneous magnetization at $p = 1/N$ which is the percolation threshold. For both {\\it directed} and {\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.2312","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"}