Indefinitely Growing Self-Avoiding Walk

Abstract

We introduce a new random walk with the property that it is strictly self-avoiding and grows forever. It belongs to a different universality class from the usual self-avoiding walk. By definition the critical exponent $\gamma$ is equal to 1. To calculate the exponent $\nu$ of the mean square end-to-end distance we have performed exact enumerations on the square lattice up to 22 steps. This gives the value $\nu =0.57\mathrm{}\pm 0.01$.