The extension of self-avoiding random walk series in two dimensions

Abstract

The authors have extended the enumeration of square lattice and triangular lattice self-avoiding walks and their end-to-end distance by two terms. They have also calculated 17 terms in the series for the resistance of SAWs with bridges on the square lattice. Analysis of the new data allows the connective constants to be more accurately estimated, and affirms the values gamma =43/32 and v=3/4, and 1+ gamma for the exponent of the resistance series.