Indefinitely Growing Self-Avoiding Walk

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 γ is equal to 1. To calculate the exponent ν 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 ν=0.57±0.01.