Corrections to scaling in 2--dimensional polymer statistics

Abstract

Writing $<R_N^2>=A{N}^{2\nu }(1+B{N}^{-{\Delta }_1}+C{N}^{-1}+...)$ for the mean square end--to--end length $<R_N^2>$ of a self--avoiding polymer chain of $N$ links, we have calculated ${\Delta }_1$ 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) $\nu =3/4$ exponent. This calculation yields ${\Delta }_1=1/2$. 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.

10 pages of RevTex, 5 Postscript figures. Accepted for publication in Phys. Rev. B. Brief Reports. Also submitted to J. Phys. A

References in corpus (1)

• Universal Amplitude Combinations for Self-Avoiding Walks, Polygons and Trails

Cited by in corpus (3)

• Correction-to-scaling exponents for two-dimensional self-avoiding walks
• An improved perturbation approach to the 2D Edwards polymer -- corrections to scaling
• Critical behaviour of the extended-ballistic transition for pulled self-avoiding walks