title: Average size of random polygons with fixed knot topology.
abstract: We have evaluated by numerical simulation the average size R(K) of random polygons of fixed knot topology K=,3(1),3(1) musical sharp 4(1), and we have confirmed the scaling law R(2)(K) approximately N(2nu(K)) for the number N of polygonal nodes in a wide range; N=100-2200. The best fit gives 2nu(K) approximately 1.11-1.16 with good fitting curves in the whole range of N. The estimate of 2nu(K) is consistent with the exponent of self-avoiding polygons. In a limited range of N (N greater, similar 600), however, we have another fit with 2nu(K) approximately 1.01-1.07, which is close to the exponent of random polygons.
authors.affiliation: Department of Physics, Faculty of Science and Engineering, Chuo University, 1-13-27 Kasuga, Bunkyo-ku, Tokyo 112-8551, Japan.
authors.forename: Hiroshi
authors.initials: H
authors.lastname: Matsuda
authors.forename: Akihisa
authors.initials: A
authors.lastname: Yao
authors.forename: Hiroshi
authors.initials: H
authors.lastname: Tsukahara
authors.forename: Tetsuo
authors.initials: T
authors.lastname: Deguchi
authors.forename: Ko
authors.initials: K
authors.lastname: Furuta
authors.forename: Takeo
authors.initials: T
authors.lastname: Inami