{"paper":{"title":"Planted vertex cover problem on regular random graphs and nonmonotonic temperature-dependence in the supercooled region","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.dis-nn","cs.IR"],"primary_cat":"cond-mat.stat-mech","authors_text":"Hai-Jun Zhou, Xin-Yi Fan","submitted_at":"2023-05-11T07:13:24Z","abstract_excerpt":"We introduce a planted vertex cover problem on regular random graphs and study it by the cavity method of statistical mechanics. Different from conventional Ising models, the equilibrium ferromagnetic phase transition of this binary-spin two-body interaction system is discontinuous, as the paramagnetic phase is separated from the ferromagnetic phase by an extensive free energy barrier. The free energy landscape can be distinguished into three different types depending on the two degree parameters of the planted graph. The critical inverse temperatures at which the paramagnetic phase becomes lo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2305.06610","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2305.06610/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"}