{"paper":{"title":"On Uniqueness of Gibbs Measures for $P$-Adic Nonhomogeneous $\\l$-Model on the Cayley Tree","license":"","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Farrukh Mukhamedov, Murod Khamraev, Utkir Rozikov","submitted_at":"2005-10-06T10:54:04Z","abstract_excerpt":"We consider a nearest-neighbor $p$-adic $\\l$-model with spin values $\\pm 1$ on a Cayley tree of order $k\\geq 1$. We prove for the model there is no phase transition and as well as the unique $p$-adic Gibbs measure is bounded if and only if $p\\geq 3$. If $p=2$ then we find a condition which guarantees nonexistence of a phase transition. Besides, the results are applied to the $p$-adic Ising model and we show that for the model there is a unique $p$-adic Gibbs measure."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0510021","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"}