{"paper":{"title":"On a spherically lifted spin model at finite temperature","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.NA","math.NA"],"primary_cat":"math.PR","authors_text":"Lexing Ying, Xun Tang, YueHaw Khoo","submitted_at":"2025-06-02T20:02:49Z","abstract_excerpt":"We investigate an \\(n\\)-vector model over \\(k\\) sites with generic pairwise interactions and spherical constraints. The model is a lifting of the Ising model whereby the support of the spin is lifted to a hypersphere. We show that the \\(n\\)-vector model converges to a limiting distribution at a rate of \\(n^{-1/2 + o(1)}\\). We show that the limiting distribution for \\(n \\to \\infty\\) is determined by the solution of an equality-constrained maximization task over positive definite matrices. We prove that the obtained maximal value and maximizer, respectively, give rise to the free energy and corr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.02220","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/2506.02220/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"}