{"paper":{"title":"The Ising magnetization exponent on Z^2 is 1/15","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":"2012-05-30T10:04:19Z","abstract_excerpt":"We prove that for the Ising model defined on the plane $\\Z^2$ at $\\beta=\\beta_c$, the average magnetization under an external magnetic field $h>0$ behaves exactly like \\[{\\sigma_0}_{\\beta_c, h} \\asymp h^{\\frac 1 {15}}\\,. \\] The proof, which is surprisingly simple compared to an analogous result for percolation (i.e. that $\\theta(p)=(p-p_c)^{5/36+o(1)}$ on the triangular lattice \\cite{\\SmirnovWerner,\\KestenScaling}) relies on the GHS inequality as well as the RSW theorem for FK percolation from \\cite{\\RSWfk}. The use of GHS to obtain inequalities involving critical exponents is not new; in this"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.6612","kind":"arxiv","version":4},"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"}