The trail problem on the square lattice

Abstract

The trail problem on the square lattice is studied by the method of exact enumeration and its relation to the self-avoiding walk problem is pointed out. The number of N-stepped trails and their mean-square sizes are enumerated on a computer up to N=17. An asymptotic analysis of the numerical data suggests that certain critical exponents obey the same values for both the trail and the self-avoiding walk problem on the square lattice.