A Monte Carlo analysis of self-avoiding walks in three dimensions

Abstract
The authors present estimates for critical exponents of self-avoiding walks on a cubic lattice. They treat a grand canonical ensemble of walks with free ends in a Monte Carlo approach and make use of real space renormalisation ideas. Their estimate for v is 0.59+or-0.01. The estimate for gamma does not share the same degree of accuracy. However, they are able to pinpoint the source of this discrepancy. In addition, they define a quantity chi L( beta ), the probability that a walk starting at the origin will end outside or at the border of a cube of side L. This quantity turns out to be quite suitable for a real space renormalisation group analysis.