{"paper":{"title":"Shattering in the Ising Pure $p$-Spin Model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Aukosh Jagannath, David Gamarnik, Eren C. K{\\i}z{\\i}lda\\u{g}","submitted_at":"2023-07-14T16:43:18Z","abstract_excerpt":"We study the Ising pure $p$-spin model for large $p$. We investigate the landscape of the Hamiltonian of this model. We show that for any $\\gamma>0$ and any large enough $p$, the model exhibits an intricate geometrical property known as the multi Overlap Gap Property above the energy value $\\gamma\\sqrt{2\\ln 2}$. We then show that for any inverse temperature $\\sqrt{\\ln 2}<\\beta<\\sqrt{2\\ln 2}$ and any large $p$, the model exhibits shattering: w.h.p. as $n\\to\\infty$, there exists exponentially many well-separated clusters such that (a) each cluster has exponentially small Gibbs mass, and (b) the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2307.07461","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/2307.07461/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"}