{"paper":{"title":"New scaling laws for self-avoiding walks: bridges and worms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.CO","math.MP"],"primary_cat":"cond-mat.stat-mech","authors_text":"Anthony J Guttmann, Bertrand Duplantier","submitted_at":"2019-08-11T08:42:31Z","abstract_excerpt":"We show how the theory of the critical behaviour of $d$-dimensional polymer networks gives a scaling relation for self-avoiding {\\em bridges} that relates the critical exponent for bridges $\\gamma_b$ to that of terminally-attached self-avoiding arches, $\\gamma_{1,1},$ and the {correlation} length exponent $\\nu.$ We find $\\gamma_b = \\gamma_{1,1}+\\nu.$ We provide compelling numerical evidence for this result in both two- and three-dimensions. Another subset of SAWs, called {\\em worms}, are defined as the subset of SAWs whose origin and end-point have the same $x$-coordinate. We give a scaling re"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.03872","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1908.03872/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"}