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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1003.2908","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2010-03-15T12:13:09Z","cross_cats_sorted":[],"title_canon_sha256":"d8c49c28c5884009f19e47be15330b9f25229d2b46f5a1b4b592b68fde2189c5","abstract_canon_sha256":"1f74b9f582fd69846d7f6d1f7a12d0dba42e7c205315e8033853c2ec633eb5ed"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:08:33.872406Z","signature_b64":"LbF2Y2cCDOIl0yMYi7esZCyxCBqfni6Ou6imdOQpGjcHdouc78guUHyXc1l1t88rW+Z/2CVqF4HR5IS3TKS3Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1656cf0a2d5957c5a28e7859fc073e4ee2d06b0b5a8eed9603debab7f6e1e09b","last_reissued_at":"2026-05-18T02:08:33.871707Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:08:33.871707Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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. 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