{"paper":{"title":"Existence of $P$-adic quasi Gibbs measure for countable state Potts model on the Cayley tree","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.FA","math.MP"],"primary_cat":"math-ph","authors_text":"Farrukh Mukhamedov","submitted_at":"2012-04-12T02:20:25Z","abstract_excerpt":"In the present paper we provide a new construction of measure, called $p$-adic quasi Gibbs measure, for countable state of $p$-adic Potts model on the Cayley tree. Such a construction depends on a parameter $\\frak{p}$ and wights. In particular case, i.e. if $\\frak{p}=\\exp_p$, the defined measure coincides with $p$-adic Gibbs measure. In this paper, under some condition on weights we establish the existence of $p$-adic quasi Gibbs measures associated with the model. Note that this condition does not depend on values of the prime $p$. An analogues fact is not valid when the number of spins is fi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.2603","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"}