{"paper":{"title":"The complexity of spherical p-spin models - a second moment approach","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Eliran Subag","submitted_at":"2015-04-09T10:43:34Z","abstract_excerpt":"Recently, Auffinger, Ben Arous, and \\v{C}ern\\'y initiated the study of critical points of the Hamiltonian in the spherical pure $p$-spin spin glass model, and established connections between those and several notions from the physics literature. Denoting the number of critical values less than $Nu$ by $\\mbox{Crt}_{N}(u)$, they computed the asymptotics of $\\frac{1}{N}\\log(\\mathbb{E}\\mbox{Crt}_{N}(u))$, as $N$, the dimension of the sphere, goes to $\\infty$. We compute the asymptotics of the corresponding second moment and show that, for $p\\geq3$ and sufficiently negative $u$, it matches the firs"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.02251","kind":"arxiv","version":2},"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"}