Twohyphen;dimensional polymeric loops ofNhard disk monomers are subject to a bending rigidity kgr;. The mean square radius of gyration lang;R2Grang;, mean area lang;Arang;, shape parameter Sgr;=lang;R2Gminrang;/lang;R2Gmaxrang;, and specific heat are studied as a function ofNand kgr;. Scaling behavior is governed by the combinationysim;N/kgr; whenN, kgr;rarr;infin;. In the rigid limit,yrarr;0, lang;R2Grang; scales asN2and 1ndash;Sgr; varies asypsgr;with psgr;=1/2. Conversely, in the soft limit,yrarr;infin;, lang;R2Grang; scales asyminus;ohgr;with ohgr;=2(1minus;ngr;)=1/2 and Sgr;rarr;0.39. The scaling domain is extended beyond the soft limit by using a nonlinear scaling field incorporating an effective rigidity kgr;tilde;(kgr;).
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