{"paper":{"title":"The critical fugacity for surface adsorption of self-avoiding walks on the honeycomb lattice is $1+\\sqrt{2}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","math.CO","math.MP"],"primary_cat":"math-ph","authors_text":"Anthony J. Guttmann, Hugo Duminil-Copin, Jan de Gier, Mireille Bousquet-M\\'elou, Nicholas R. Beaton","submitted_at":"2011-09-02T05:07:07Z","abstract_excerpt":"In 2010, Duminil-Copin and Smirnov proved a long-standing conjecture of Nienhuis, made in 1982, that the growth constant of self-avoiding walks on the hexagonal (a.k.a. honeycomb) lattice is $\\mu=\\sqrt{2+\\sqrt{2}}.$ A key identity used in that proof was later generalised by Smirnov so as to apply to a general O(n) loop model with $n\\in [-2,2]$ (the case $n=0$ corresponding to SAWs).\n  We modify this model by restricting to a half-plane and introducing a surface fugacity $y$ associated with boundary sites (also called surface sites), and obtain a generalisation of Smirnov's identity. The critic"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.0358","kind":"arxiv","version":5},"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"}