End-to-end distance distributions and asymptotic behaviour of self-avoiding walks in two and three dimensions

Publisher Website
Google Scholar
Abstract
We use Monte Carlo methods to study the reduced moments and full end-to-end distance distributions of self-avoiding walks in two and three dimensions. We find that the reduced moments scale with length via delta pg=A+B/N( Delta pq) with corrections to the scaling exponents that vary with the order of the moment. We also find that the complete end-to-end distance distributions are well described by a Redner-des Cloizeaux (RdC) model qN(x)=Cx( theta N)exp(-(Kx)(tN)), x being the rescaled length. We develop a method that allows reliable estimation of the exponents theta N and tN from the extrapolated reduced moments and use this method to extrapolate to chain lengths beyond those investigated here. We find that, in three dimensions, the optimal tN, for N>1000 is smaller than the theoretically expected value t=2.445. This implies that care must be taken in using the RdC ansatz to interpret the behaviour of self-avoiding walks, even in the asymptotic limit.