{"paper":{"title":"On the probability of staying above a wall for the (2+1)-dimensional SOS model at low temperature","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Fabio Lucio Toninelli, Fabio Martinelli, Pietro Caputo","submitted_at":"2014-06-04T20:40:51Z","abstract_excerpt":"We obtain sharp asymptotics for the probability that the (2+1)-dimensional discrete SOS interface at low temperature is positive in a large region. For a square region $\\Lambda$, both under the infinite volume measure and under the measure with zero boundary conditions around $\\Lambda$, this probability turns out to behave like $\\exp(-\\tau_\\beta(0) L \\log L )$, with $\\tau_\\beta(0)$ the surface tension at zero tilt, also called step free energy, and $L$ the box side. This behavior is qualitatively different from the one found for continuous height massless gradient interface models."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.1206","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"}