{"paper":{"title":"The Order of Free Energy Fluctuations in the Critical Sherrington-Kirkpatrick Model Revisited","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Adrien Schertzer","submitted_at":"2026-06-19T12:04:08Z","abstract_excerpt":"We study the fluctuations of the free energy of the Sherrington-Kirkpatrick model at the critical inverse temperature $\\beta=1$. We prove that \\[ \\operatorname{Var}(F_N(1))\\leq \\frac14\\log N+C, \\] with $C$ independent of $N$. This gives a logarithmic upper bound, in agreement with the order predicted in the physics literature. We also prove that the critical variance diverges: more precisely, \\[ \\operatorname{Var}(F_N(1)) \\geq \\frac12\\log\\log\\log N - C . \\]"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.21360","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/2606.21360/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"}