Anomalous finite-size effects for the mean-squared gyration radius of Gaussian random knots

Abstract

Anomalously strong finite-size effects have been observed for the mean square radius of gyration R2K of Gaussian random polygons with a fixed knot K as a function of the number N of polygonal nodes. Through computer simulations with N<2000, we find that the gyration radius R2K can be approximated by a power law, R2K ~ N2νKeff, for several knots, where the effective exponents νKeff are larger than 0.5 and less than 0.6. Furthermore, a crossover occurs for the gyration radius of the trivial knot, when N is roughly equal to the characteristic length Nc of random knotting. Assuming an asymptotic fitting formula, we also discuss possible asymptotic behaviours for RK2 of Gaussian random polygons.