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

The dynamics of the fraction of never flipped spins F(t) and the average domain area A(t) of the two-dimensional, infinite-Q Potts model are investigated by zero-temperature Monte Carlo simulations. It is shown that the exponents α of algebraic growth of A(t) and Θ of algebraic decay of F(t) are only effective exponents even for very large systems and long times. Their values increase from about 0.9 for short times to almost unity at late times. The fraction of never flipped spins follows a much better power law when viewed as a function of the average domain area, which is the characteristic size in the system. An exponent of Θ′ = 0.98 ± 0.01 is obtained for the decay of F(A) in the whole time interval, consistent with linear behavior.