{"paper":{"title":"Ising critical behavior of inhomogeneous Curie-Weiss models and annealed random graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Claudio Giberti, Cristian Giardin\\`a, Maria Luisa Prioriello, Remco van der Hofstad, Sander Dommers","submitted_at":"2015-09-24T11:52:33Z","abstract_excerpt":"We study the critical behavior for inhomogeneous versions of the Curie-Weiss model, where the coupling constant $J_{ij}(\\beta)$ for the edge $ij$ on the complete graph is given by $J_{ij}(\\beta)=\\beta w_iw_j/(\\sum_{k\\in[N]}w_k)$. We call the product form of these couplings the rank-1 inhomogeneous Curie-Weiss model. This model also arises (with inverse temperature $\\beta$ replaced by $\\sinh(\\beta)$) from the annealed Ising model on the generalized random graph. We assume that the vertex weights $(w_i)_{i\\in[N]}$ are regular, in the sense that their empirical distribution converges and the seco"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.07327","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"}