Dynamical Behavior of Persistent Spins in the Triangular Potts Model

This article summarizes the results of a series of Monte Carlo simulations of persistent spins or “survivors” in the triangular Q-state Potts model. It is shown that the fraction F(t) of survivors decays algebraically in time t, with nontrivial exponents θ depending on Q but not on temperature T. At zero temperature, asymptotic exponents θ have been calculated for the whole range of Q = 3 to ∞. In accordance with exact results in one dimension and early Monte Carlo studies in two dimensions, θ increases from 0.31 to unity as Q increases from 3 to ∞. For small Q, it has also been shown that θ approaches the same universal value for both zero and non-zero temperatures (below the critical temperature Tc).