{"paper":{"title":"Periodic $p$-adic Gibbs measures of $q$-states Potts model on Cayley tree: The chaos implies the vastness of $p$-adic Gibbs measures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Lingmin Liao (LAMA), Mansoor Saburov, Mohd Ali Khameini Ahmad (LAMA)","submitted_at":"2017-08-07T15:06:31Z","abstract_excerpt":"We study the set of $p$-adic Gibbs measures of the $q$-states Potts model on the Cayley tree of order three. We prove the vastness of the periodic $p$-adic Gibbs measures for such model by showing the chaotic behavior of the correspondence Potts--Bethe mapping over $\\mathbb{Q}\\_p$ for $p\\equiv 1 \\ (\\rm{mod} \\ 3)$. In fact, for $0 < |\\theta-1|\\_p < |q|\\_p^2 < 1$, there exists a subsystem that isometrically conjugate to the full shift on three symbols. Meanwhile, for $0 < |q|\\_p^2 \\leq |\\theta-1|\\_p < |q|\\_p < 1$, there exists a subsystem that isometrically conjugate to a subshift of finite type"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.02152","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"}