{"paper":{"title":"Renewal properties of the $d=1$ Ising model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Errico Presutti, Immacolata Merola, Marzio Cassandro","submitted_at":"2017-10-06T15:57:56Z","abstract_excerpt":"We consider the $d=1$ Ising model with Kac potentials at inverse temperature $\\beta>1$ where mean field predicts a phase transition with two possible equilibrium magnetization $\\pm m_\\beta$, $m_\\beta>0$. We show that when the Kac scaling parameter $\\gamma$ is sufficiently small typical spin configurations are described (via a coarse graining) by an infinite sequence of successive plus and minus intervals where the empirical magnetization is \"close\" to $m_\\beta$ and respectively $-m_\\beta$. We prove that the corresponding marginal of the unique DLR measure is a renewal process."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.02466","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"}