An improved perturbation approach to the 2D Edwards polymer -- corrections to scaling

Abstract

We present the results of a new perturbation calculation in polymer statistics which starts from a ground state that already correctly predicts the long chain length behaviour of the mean square end--to--end distance $\langle R_N^2 \rangle\ $, namely the solution to the 2~dimensional~(2D) Edwards model. The $\langle R_N^2 \rangle$ thus calculated is shown to be convergent in $N$, the number of steps in the chain, in contrast to previous methods which start from the free random walk solution. This allows us to calculate a new value for the leading correction--to--scaling exponent~$Δ$. Writing $\langle R_N^2 \rangle = AN^{2ν}(1+BN^{-Δ} + CN^{-1}+...)$, where $ν= 3/4$ in 2D, our result shows that $Δ= 1/2$. This value is also supported by an analysis of 2D self--avoiding walks on the {\em continuum}.