{"paper":{"title":"Layered systems at the mean field critical temperature","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Domingos H. U. Marchetti, Errico Presutti, Immacolata Merola, Luiz Renato Fontes, Maria Eulalia Vares","submitted_at":"2015-04-25T22:36:54Z","abstract_excerpt":"We consider the Ising model on $\\mathbb Z\\times \\mathbb Z$ where on each horizontal line $\\{(x,i), x\\in \\mathbb Z\\}$, the interaction is given by a ferromagnetic Kac potential with coupling strength $J_\\gamma(x,y)\\sim \\gamma J(\\gamma (x-y))$ at the mean field critical temperature. We then add a nearest neighbor ferromagnetic vertical interaction of strength $\\epsilon$ and prove that for every $\\epsilon >0$ the systems exhibits phase transition provided $\\gamma>0$ is small enough."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.06767","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"}