{"paper":{"title":"Eigenvalue amplitudes of the Potts model on a torus","license":"","headline":"","cross_cats":["cond-mat.stat-mech","math.CO","math.MP"],"primary_cat":"math-ph","authors_text":"Jean-Francois Richard (LPTMS, Jesper Lykke Jacobsen (LPTMS, LPTHE), SPhT)","submitted_at":"2006-08-23T18:18:05Z","abstract_excerpt":"We consider the Q-state Potts model in the random-cluster formulation, defined on finite two-dimensional lattices of size L x N with toroidal boundary conditions. Due to the non-locality of the clusters, the partition function Z(L,N) cannot be written simply as a trace of the transfer matrix T\\_L. Using a combinatorial method, we establish the decomposition Z(L,N) = \\sum\\_{l,D\\_k} b^{l,D\\_k} K\\_{l,D\\_k}, where the characters K\\_{l,D\\_k} = \\sum\\_i (\\lambda\\_i)^N are simple traces. In this decomposition, the amplitudes b^{l,D\\_k} of the eigenvalues \\lambda\\_i of T\\_L are labelled by the number l"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0608055","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-ph/0608055/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"}