{"paper":{"title":"On factors associated with quantum Markov states corresponding to nearest neighbor models on a Cayley tree","license":"","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.OA","authors_text":"Farruh Mukhamedov, Francesco Fidaleo","submitted_at":"2004-11-09T15:54:00Z","abstract_excerpt":"In this paper we consider nearest neighbour models where the spin takes values in the set $\\Phi=\\{\\z_1,\\z_2,...,\\z_q\\}$ and is assigned to the vertices of the Cayley tree ${\\G}^k$. The Hamiltonian is defined by some given $\\lambda$-function. We find a condition for the function $\\lambda$ to determine the type of the von Neumann algebra generated by the GNS - construction associated with the quantum Markov state corresponding to the unordered phase of the $\\lambda$-model. Also we give some physical applications of the obtained result."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0411196","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/math/0411196/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"}