{"paper":{"title":"Phase separation for the long range one--dimensional ising model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Immacolata Merola, Marzio Cassandro, Pierre Picco","submitted_at":"2016-11-07T21:32:13Z","abstract_excerpt":"We consider the phase separation problem for the one--dimensional ferromagnetic Ising model with long--range two--body interaction, $J(n)=n^{-2+\\a}$ where $n\\in \\N$ denotes the distance of the two spins and $ \\alpha \\in ]0,\\a_+[$ with $\\a_+=(\\log 3)/(\\log 2) -1$. We prove that given $m\\in ]-1,+1[$, if the temperature is small enough, then typical configuration for the $\\mu^{+}$ Gibbs measure conditionally to have a empirical magnetization of the order $m$ are made of a single interval that occupy almost a proportion $\\frac{1}{2}(1-\\frac{m}{m_\\b})$ of the volume with the minus phase inside and "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.02310","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"}