Monte Carlo series analysis of irreversible self-avoiding walks. I. The indefinitely-growing self-avoiding walk (IGSAW)

Abstract

High-precision Monte Carlo data are used to estimate the exponents which govern the asymptotic behaviour of the recently introduced indefinitely-growing self-avoiding walk in two dimensions. For this walk the exponent gamma is by definition equal to one. Applying the same methods which are used to extract the exponents from exact series enumeration, the authors give an estimate for the exponent nu of 0.567+or-0.003. The leading corrections to this asymptotic behaviour are also calculated.