{"paper":{"title":"KMS states and branched points","license":"","headline":"","cross_cats":["math.DS"],"primary_cat":"math.OA","authors_text":"Masaki Izumi, Tsuyoshi Kajiwara, Yasuo Watatani","submitted_at":"2006-03-25T07:08:50Z","abstract_excerpt":"We completely classify the KMS states for the gauge action on a $C^*$-algebra associated with a rational function $R$ introduced in our previous work. The gauge action has a phase transition at $\\beta = \\log \\deg R$. We can recover the degree of $R$, the number of branched points, the number of exceptional points and the orbits of exceptional points from the structure of the KMS states. We also classify the KMS states for $C^*$-algebras associated with some self-similar sets, including the full tent map and the Sierpinski gasket by a similar method."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0603592","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/0603592/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"}