On self-repelling walks

Abstract
The authors investigate the properties of self-repelling walks-otherwise known as 'true' self-avoiding walks-in both one and two dimensions for a range of values of the repulsion parameter g, 0.2N2), while on the two-dimensional square lattice they have obtained 12-15 terms. In one dimension they find the data to be well fitted by (RN2)=N43/(A+B/N13/+C/N+O(1/N)) and in two dimensions by (RN2)=DN mod lnN mod alpha (1+0(ln mod lnN mod /lnN)) with alpha approximately=0.5. Estimates of the amplitudes A and D are also obtained.