Survivors in the two-dimensional Potts model: zero-temperature dynamics for finite Q

The Q-dependence of the dynamics of the fraction of never flipped 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 [Hennecke, Physica A 246 (1997) 519] for Q=∞ to finite Q, asymptotic values of the exponents α of algebraic growth of A(t) and θ of algebraic decay of F(t) are determined. Effective exponents α increase with time to an asymptotic value α ≈ 1, independently of Q. In contrast, asymptotic values of θ do depend on Q and increase from 0.31 to unity when Q increases from 3 to ∞.