Average size of random polygons with fixed knot topology
Hiroshi Matsuda, Akihisa Yao, Hiroshi Tsukahara, Tetsuo Deguchi, Ko Furuta, Takeo Inami
Abstract
We have evaluated by numerical simulation the average size
R
K
of random polygons of fixed knot topology
K=∅,
3
1
,
3
1
♯
4
1
, and we have confirmed the scaling law
R
2
K
∼
N
2
ν
K
for the number
N
of polygonal nodes in a wide range;
N=100
-- 2200. The best fit gives
2
ν
K
≃1.11
-- 1.16 with good fitting curves in the whole range of
N
. The estimate of
2
ν
K
is consistent with the exponent of self-avoiding polygons. In a limited range of
N
(
N≳600
), however, we have another fit with
2
ν
K
≃1.01
-- 1.07, which is close to the exponent of random polygons.