{"paper":{"title":"Conformal partition functions of critical percolation from $D_3$ Thermodynamic Bethe Ansatz equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math-ph","math.MP"],"primary_cat":"cond-mat.stat-mech","authors_text":"Alexi Morin-Duchesne, Andreas Kl\\\"umper, Paul A. Pearce","submitted_at":"2017-01-27T19:00:05Z","abstract_excerpt":"Using the planar Temperley-Lieb algebra, critical bond percolation on the square lattice is incorporated as ${\\cal LM}(2,3)$ in the family of Yang-Baxter integrable logarithmic minimal models ${\\cal LM}(p,p')$. We consider this model in the presence of boundaries and with periodic boundary conditions. Inspired by Kuniba, Sakai and Suzuki, we rewrite the recently obtained infinite $Y$-system of functional equations. We obtain nonlinear integral equations in the form of a closed finite set of TBA equations described by a $D_3$ Dynkin diagram. Following the methods of Kl\\\"umper and Pearce, we sol"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.08167","kind":"arxiv","version":2},"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"}