Critical exponents of self-avoiding walks in three dimensions.

Abstract

We analyze Monte Carlo data of self-avoiding walks with up to about 8000 steps on a simple cubic lattice with emphasis on the question of the discrepancy between the scaling exponents obtained by renormalization group calculations and Monte Carlo simulations. This discrepancy has been recently investigated by Dayantis and Palierne [Phys. Rev. B 49, 3217 (1994)] for self-avoiding walks of up to 3000 steps, and has been shown to originate from the finite size of chains generated in Monte Carlo simulations. Our analysis demonstrates this conjecture and shows that the exponents decrease for longer chains toward the renormalization group value.