Corrections to scaling in 2--dimensional polymer statistics

Abstract

Writing $<R^2_N > = AN^{2ν}(1+BN^{-Δ_1}+CN^{-1}+ ...)$ for the mean square end--to--end length $<R^2_N>$ of a self--avoiding polymer chain of $N$ links, we have calculated $Δ_1$ for the two--dimensional {\em continuum} case from a new {\em finite} perturbation method based on the ground state of Edwards self consistent solution which predicts the (exact) $ν=3/4$ exponent. This calculation yields $Δ_1=1/2$. A finite size scaling analysis of data generated for the continuum using a biased sampling Monte Carlo algorithm supports this value, as does a re--analysis of exact data for two--dimensional lattices.