A new Monte-Carlo approach to the critical properties of self-avoiding random walks

Abstract

We investigate the critical properties of self-avoiding random walks on hypercubic lattices in dimensions three and four. We consider the statistical ensembles of all such walks as a function of an inverse temperature β and associate to each walk the statistical weight βL, where L is its length. This allows us to use a novel and very efficient Monte-Carlo procedure. A new interpretation of the exponent γ, suitable for numerical investigations, is presented. In dimension four, the logarithmic violations predicted by the perturbative renormalization group are very well verified