{"paper":{"title":"Polygons in restricted geometries subjected to infinite forces","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":"Christine E Soteros, Jeremy W Eng, Nicholas R Beaton","submitted_at":"2016-04-25T22:31:24Z","abstract_excerpt":"We consider self-avoiding polygons in a restricted geometry, namely an infinite $L\\times M$ tube in $\\mathbb Z^3$. These polygons are subjected to a force $f$, parallel to the infinite axis of the tube. When $f>0$ the force stretches the polygons, while when $f<0$ the force is compressive. We obtain and prove the asymptotic form of the free energy in both limits $f\\to\\pm\\infty$. We conjecture that the $f\\to-\\infty$ asymptote is the same as the limiting free energy of \"Hamiltonian\" polygons, polygons which visit every vertex in a $L\\times M\\times N$ box. We investigate such polygons, and in par"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.07465","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":""},"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"}