{"paper":{"title":"On Inhomogeneous $p$-Adic Potts Model on a Cayley Tree","license":"","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Farrukh Mukhamedov, Utkir Rozikov","submitted_at":"2005-10-06T14:12:22Z","abstract_excerpt":"We consider a nearest-neighbor inhomogeneous $p$-adic Potts (with $q\\geq 2$ spin values) model on the Cayley tree of order $k\\geq 1$. The inhomogeneity means that the interaction $J_{xy}$ couplings depend on nearest-neighbors points $x, y $ of the Cayley tree. We study ($p-$ adic) Gibbs measures of the model. We show that (i) if $q\\notin p\\mathbb{N}$ then there is unique Gibbs measure for any $k\\geq 1$ and $\\forall J_{xy}$ with $|J_{xy}|<p^{-1/(p-1)}$. (ii) For $q\\in p\\mathbb{N}, p\\geq 3$ one can choose $J_{xy}$ and $k\\geq 1$ such that there exist at least two Gibbs measures which are translat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0510024","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":""},"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"}