The excluded volume effect for self-avoiding random walks

Abstract

A method is developed to predict the asymptotic behavior of totally self‐avoiding walks by utilizing data for random walks of limited orders of nonself intersection. The results shed further light on the exponent, γ, in the equation for the mean square end‐to‐end separation : <R_N²≳∼N^γ, where γ=3/2 in two dimensions and γ=6/5 in three. The prediction of γ is achieved by analyzing the slopes and intercepts of the asymptotes of <R_N²≳ for limited order walks. To obtain accurate estimates of the slopes of such asymptotes, a new Monte Carlo sampling method has been developed. Calculations using such Monte Carlo simulation for finite order walks are used to predict the generally accepted self‐avoiding behavior.