{"paper":{"title":"Asymptotic behaviour of convex and column-convex lattice polygons with fixed area and varying perimeter","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"Gautam I Menon, Mithun K Mitra, R Rajesh","submitted_at":"2010-03-15T12:13:09Z","abstract_excerpt":"We study the inflated phase of two dimensional lattice polygons, both convex and column-convex, with fixed area A and variable perimeter, when a weight \\mu^t \\exp[- Jb] is associated to a polygon with perimeter t and b bends. The mean perimeter is calculated  as a function of the fugacity \\mu and the bending rigidity J. In the limit \\mu -> 0, the mean perimeter has the asymptotic behaviour \\avg{t}/4 \\sqrt{A} \\simeq 1 - K(J)/(\\ln \\mu)^2 + O (\\mu/ \\ln \\mu) . The constant K(J) is found to be the same for both types of polygons, suggesting that self-avoiding polygons should also exhibit the same a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1003.2908","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"}