{"paper":{"title":"Phase Transitions in Ferromagnetic Ising Models with spatially dependent magnetic fields","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":["math.MP","math.PR"],"primary_cat":"math-ph","authors_text":"Errico Presutti, Leandro Cioletti, Marzio Cassandro, Rodrigo Bissacot","submitted_at":"2014-03-31T11:59:18Z","abstract_excerpt":"In this paper we study the nearest neighbor Ising model with ferromagnetic interactions in the presence of a space dependent magnetic field which vanishes as $|x|^{-\\alpha}$, $\\alpha >0$, as $|x|\\to \\infty$. We prove that in dimensions $d\\ge 2$ for all $\\beta$ large enough if $\\alpha>1$ there is a phase transition while if $\\alpha<1$ there is a unique DLR state."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.7961","kind":"arxiv","version":3},"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"}