A Monte Carlo study of non-trapped self-avoiding walks

Abstract

In this paper, we study non-trapped self-avoiding walks (SAWs), which are SAWs that can be extended to an arbitrary length. We apply the flatPERM Monte Carlo method for this purpose, generating non-trapped SAWs of length up to 1024 on the square, triangular and hexagonal lattices, and calculating their number and mean squared end-to-end distance. We find strong numerical evidence that the growth constant μ and entropic and metric exponents γ and ν are identical for non-trapped and all SAWs, and in particular that the exponents are also universal for non-trapped SAWs. We also calculate the limiting ratio of non-trapped to all SAWs. We see some evidence of an n 1/2 correction-to-scaling term w..