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 $⟨R_N^2⟩$, namely the solution to the 2~dimensional~(2D) Edwards model. The $⟨R_N^2⟩$ 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 $⟨R_N^2⟩=A{N}^{2\nu }(1+B{N}^{-\Delta }+C{N}^{-1}+...)$, 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}.

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

References in corpus (2)

• Universal Amplitude Combinations for Self-Avoiding Walks, Polygons and Trails
• Corrections to scaling in 2--dimensional polymer statistics