THE COLLAPSE POINT OF INTERACTING TRAILS IN 2 DIMENSIONS FROM KINETIC GROWTH SIMULATIONS

We present simulational evidence that kinetic growth trails on the square lattice are equivalent to interacting trails at their collapse temperature. As a consequence we give values for most of the canonical exponents of the trail collapse transition: these are significantly different from those proposed for interacting walks. We can also interpret our results in terms of the equivalent Lorentz lattice gas and find that this model does not display diffusion, as has been previously thought. Rather, the mean square displacement grows as t log t in time t.