{"paper":{"title":"The Jordan Structure of Two Dimensional Loop Models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","math.MP"],"primary_cat":"math-ph","authors_text":"Alexi Morin-Duchesne, Yvan Saint-Aubin","submitted_at":"2011-01-14T20:30:04Z","abstract_excerpt":"We show how to use the link representation of the transfer matrix $D_N$ of loop models on the lattice to calculate partition functions, at criticality, of the Fortuin-Kasteleyn model with various boundary conditions and parameter $\\beta = 2 \\cos(\\pi(1-a/b)), a,b\\in \\mathbb N$ and, more specifically, partition functions of the corresponding $Q$-Potts spin models, with $Q=\\beta^2$. The braid limit of $D_N$ is shown to be a central element $F_N(\\beta)$ of the Temperley-Lieb algebra $TL_N(\\beta)$, its eigenvalues are determined and, for generic $\\beta$, a basis of its eigenvectors is constructed u"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.2885","kind":"arxiv","version":4},"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"}