University of Arizona

The self-avoiding walk is a random walk that is not allowed to

visit the same site more than once. The distance from the starting

point to the end point is a random variable whose variance is

believed to scale like the number of steps in the walk raised to

the 3/2 power in two dimensions. We present the results of

Monte Carlo simulations of this model on several different

two-dimensional lattices. They show that the distribution of this

walk does not depend on the lattice in the limit that the number of

steps goes to infinity.