{"paper":{"title":"Inapproximability After Uniqueness Phase Transition in Two-Spin Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Heng Guo, Jin-Yi Cai, Pinyan Lu, Xi Chen","submitted_at":"2012-05-14T03:10:28Z","abstract_excerpt":"A two-state spin system is specified by a 2 x 2 matrix\n  A = {A_{0,0} A_{0,1}, A_{1,0} A_{1,1}} = {\\beta 1, 1 \\gamma}\nwhere \\beta, \\gamma \\ge 0. Given an input graph G=(V,E), the partition function Z_A(G) of a system is defined as\n  Z_A(G) = \\sum_{\\sigma: V -> {0,1}} \\prod_{(u,v) \\in E} A_{\\sigma(u), \\sigma(v)}\n  We prove inapproximability results for the partition function in the region specified by the non-uniqueness condition from phase transition for the Gibbs measure. More specifically, assuming NP \\ne RP, for any fixed \\beta, \\gamma in the unit square, there is no randomized polynomial-t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.2934","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"}