Corrections to scaling in 2--dimensional polymer statistics

TL;DR

This paper determines the correction-to-scaling exponent for 2D self-avoiding polymers using a new perturbation method and supports the findings with Monte Carlo simulations and lattice data analysis.

Contribution

It introduces a finite perturbation approach to calculate the correction-to-scaling exponent in 2D polymer statistics, confirming the value as 1/2.

Findings

Calculated correction-to-scaling exponent Δ₁=1/2 for 2D polymers.

Supported the theoretical prediction with Monte Carlo simulations.

Re-analyzed lattice data confirming the exponent value.

Abstract

Writing $<R^2_N > = AN^{2\nu}(1+BN^{-\Delta_1}+CN^{-1}+ ...)$ for the mean square end--to--end length $<R^2_N>$ of a self--avoiding polymer chain of $N$ links, we have calculated $\Delta_1$ 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.