{"paper":{"title":"Lower Bounds and Series for the Ground State Entropy of the Potts Antiferromagnet on Archimedean Lattices and their Duals","license":"","headline":"","cross_cats":["hep-lat","math.CO"],"primary_cat":"cond-mat.stat-mech","authors_text":"Robert Shrock, Shan-Ho Tsai (Institute for Theoretical Physics, State University of New York at Stony Brook)","submitted_at":"1997-07-29T21:56:23Z","abstract_excerpt":"We prove a general rigorous lower bound for $W(\\Lambda,q)=\\exp(S_0(\\Lambda,q)/k_B)$, the exponent of the ground state entropy of the $q$-state Potts antiferromagnet, on an arbitrary Archimedean lattice $\\Lambda$. We calculate large-$q$ series expansions for the exact $W_r(\\Lambda,q)=q^{-1}W(\\Lambda,q)$ and compare these with our lower bounds on this function on the various Archimedean lattices. It is shown that the lower bounds coincide with a number of terms in the large-$q$ expansions and hence serve not just as bounds but also as very good approximations to the respective exact functions $W"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/9707306","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/cond-mat/9707306/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"}