END-TO-END DISTANCE DISTRIBUTIONS AND ASYMPTOTIC-BEHAVIOR OF SELF-AVOIDING WALKS IN 2 AND 3 DIMENSIONS

We use Monte Carlo methods to study the reduced moments and full end-t o-end distance distributions of self-avoiding walks in two and three d imensions. We find that the reduced moments scale with length via delt a(pq) = A + B/N-Delta pq with corrections to the scaling exponents tha t vary with the order of the moment. We also find that the complete en d-to-end distance distributions are well described by a Redner-des Clo izeaux (RdC) model q(N)(x) = C x(theta N) exp(-(Kx)(tN)) [1,2], x bein g the rescaled length. We develop a method that allows reliable estima tion of the exponents theta(N) and t(N) from the extrapolated reduced moments and use this method to extrapolate to chain lengths beyond tho se investigated here. We find that, in three dimensions, the optimal t (N) 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 asymptoti c limit.