{"paper":{"title":"Planar Ising magnetization field II. Properties of the critical and near-critical scaling limits","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Charles M. Newman, Christophe Garban, Federico Camia","submitted_at":"2013-07-15T13:17:08Z","abstract_excerpt":"In [CGN12], we proved that the renormalized critical Ising magnetization fields $\\Phi^a:= a^{15/8} \\sum_{x\\in a\\, \\Z^2} \\sigma_x \\, \\delta_x$ converge as $a\\to 0$ to a random distribution that we denoted by $\\Phi^\\infty$. The purpose of this paper is to establish some fundamental properties satisfied by this $\\Phi^\\infty$ and the near-critical fields $\\Phi^{\\infty,h}$. More precisely, we obtain the following results. \\bi [(i)] If $A\\subset \\C$ is a smooth bounded domain and if $m=m_A := <{\\Phi^\\infty, 1_A}$ denotes the limiting rescaled magnetization in $A$, then there is a constant $c=c_A>0$ "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.3926","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"}