Survivors in the two - dimensional Potts model : Zero temperature dynamics for nite

The Q-dependence of the dynamics of the fraction of never ipped spins F(t) and the average domain area A(t) of the triangular Q-state Potts model are investigated by zero temperature Monte Carlo simulations. Extending a recent study Physica A246 (1997), 519] for Q = 1 to nite Q, asymptotic values of the exponents of algebraic growth of A(t) and of algebraic decay of F(t) are determined. EEective exponents increase with time to an asymptotic value 1, independently of Q. In contrast, asymptotic values of do depend on Q and increase from 0:31 to unity when Q increases from 3 to 1. Zero temperataure dynamics of the Potts model have been re-investigated in recent years, since Derrida et al..1] discovered that the fraction F(t) of spins which have not ipped until time t exhibits non-trivial dynamical behavior. In one dimension, they showed that F(t) decays algebraically, F(t) t ? (1) with varying continuously between zero and one as Q increases from 1 to 1 1,2]. Derrida et al..3] studied the problem in two dimensions by Monte Carlo simulations. However, their results for high Q are inaccurate since the data showed some curvature and only eeective exponents for could be determined. We recently investigated the two-dimensional Potts model for Q = 1 by a similar zero temperature Monte Carlo method, see Ref. 4] and references 1 Permanent address.