EXPONENTS APPEARING IN THE ZERO-TEMPERATURE DYNAMICS OF THE 1D POTTS-MODEL

For the Glauber dynamics of the one-dimensional q-state Potts model at zero temperature, the fraction of spins which have never dipped up to time t decreases as t(-theta(q)) where the exponent theta(q) varies c ontinuously with q. The calculation of the q dependence of this expone nt can be reduced to the study of a simple reaction-diffusion model. U sing finite-size scaling, this allows one to obtain accurate estimates of theta(q) for all values of q. One can also show that for q = 1 + e psilon, the expansion of theta(q) is given by theta(q) = (2/pi)epsilon + O(epsilon(2)).