New exponent in self-avoiding walks

Abstract

A new exponent is reported in the problem of non-intersecting self-avoiding random walks. It is connected with the asymptotic behaviour of the growth of number of such walks. The value of the exponent is found to be nearly 0.90 for all two dimensional and nearly 0.96 for all three dimensional, lattices studied here. It approaches the value 1.0 assymptotically as the dimensionality approaches infinity. © 1984 Springer-Verlag.