{"paper":{"title":"Order of Fluctuations of the Free Energy in the SK Model at Critical Temperature","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Wai-Kit Lam, Wei-Kuo Chen","submitted_at":"2019-01-29T02:21:44Z","abstract_excerpt":"We present an elementary approach to the order of fluctuations for the free energy in the Sherrington-Kirkpatrick mean field spin glass model at and near the critical temperature. It is proved that at the critical temperature the variance of the free energy is of $O((\\log N)^2).$ In addition, we show that if one approaches the critical temperature from the low temperature regime at the rate $O(N^{-\\alpha})$ for some $\\alpha>0,$ then the variance is of $O((\\log N)^2+N^{1-\\alpha}).$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.10070","kind":"arxiv","version":3},"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"}