{"paper":{"title":"Structure of 1-RSB asymptotic Gibbs measures in the diluted p-spin models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Dmitry Panchenko","submitted_at":"2013-08-08T19:44:23Z","abstract_excerpt":"In this paper we study asymptotic Gibbs measures in the diluted p-spin models in the so called 1-RSB case, when the overlap takes two values $q_*, q^*\\in [0,1].$ When the external field is not present and the overlap is not equal to zero, we prove that such asymptotic Gibbs measures are described by the M\\'ezard-Parisi ansatz conjectured in [MP]. When the external field is present, we prove that the overlap can not be equal to zero and all 1-RSB asymptotic Gibbs measures are described by the M\\'ezard-Parisi ansatz. Finally, we give a characterization of the exceptional case when there is no ex"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.1944","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":""},"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"}