{"paper":{"title":"A note on Lata\\la's argument in SK model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Seiichiro Kusuoka, Shuta Nakajima","submitted_at":"2026-07-26T02:54:45Z","abstract_excerpt":"In this note, we consider the Sherrington--Kirkpatrick model with deterministic external field. Let $q=q(\\beta,h)$ denote the solution of the replica-symmetric self-consistency equation \\[ q=\\mathbb E\\tanh^2\\!\\left(h+\\beta\\sqrt q\\,Z\\right), \\qquad Z\\sim N(0,1), \\] where $\\beta$ and $h$ are inverse temperature and external field, respectively.\n  By refining Lata\\la' s argument, previously limited to \\(\\beta < \\frac{1}{2}\\), and using the Kearns--Saul inequality, we prove overlap concentration and convergence of the free energy to the replica symmetric formula with error \\(O(N^{-1})\\) whenever\n "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.23427","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.23427/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}