The geometrical properties of planar lattice trails

Abstract

The authors investigate the winding angle and mean square end-to-end distance of lattice trails on a square lattice, by both exact enumeration and Monte Carlo methods. They find similar behaviour to that of self-avoiding walks, to the extent that the complete distribution is found to agree with the recent exact calculation of the winding-angle distribution function for self-avoiding walks by Duplantier and Saleur (1988), who found a Gaussian distribution. The exponent nu was found to be indistinguishable from 3/4.