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

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

1995-11-02

arxiv.org/abs/cond-mat/9511010v1

Physics

Condensed Matter

17 Pages of Revtex. No figures. Submitted to J. Phys. A

Scientific paper

10.1063/1.472625

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~$\Delta$. Writing $\langle R_N^2 \rangle = AN^{2\nu}(1+BN^{-\Delta} + CN^{-1}+...)$, where $\nu = 3/4$ in 2D, our result shows that $\Delta = 1/2$. This value is also supported by an analysis of 2D self--avoiding walks on the {\em continuum}.

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