NONTRIVIAL EXPONENTS IN THE ZERO-TEMPERATURE DYNAMICS OF THE 1D ISING AND POTTS MODELS

We consider the Glauber dynamics of the q-state Potts model in one dimension at zero temperature. Starting with a random initial configuration, we measure the density r(t) of spins which have never flipped from the beginning of the simulation until time t. We find that for large t, the density r(t) has a power-law decay (r(t) approximately t(-theta)) where the exponent theta varies with q. Our simulations lead to theta congruent-to 0.37 for q = 2, theta congruent-to 0.53 for q = 3 and theta --> 1 as q --> infinity.