Universality of Derrida Coarsening in the Triangular Potts Model

The temperature dependence of the dynamics of the fraction F (t) of persistent spins in the triangular Q-state Potts model is investigatedby large scale Monte Carlo simulations. After extending Derrida's approach of measuring the fraction of spins that remain in one phase to all Q low-temperaturephases, it is shown that the exponent of algebraic decay of F (t) is independent of temperature. In the zero temperature Potts model, persistent spins or \survivors" are the fraction F(t) of spins which have not ipped until time t when the system evolves under a single-spin-ip dynamics. Derrida et al. 1;2 have shown that in one dimension , F(t) decays algebraically with an exponent varying continuously between zero and one as Q increases from 1 to 1. In two dimensions, early Monte Carlo simulations by Derrida et al. 3 connrmed the Q-dependence of the exponent , but suuered from blocking eeects on the square lattice. Additionally, results for high Q were inaccurate due to curvature in the log-log plots. By large scale Monte Carlo simulations of the triangular Potts model where the vertex dynamics does not suuer from blocking, we have recently connrmed 4;5 that in two dimensions, also varies continuously with Q and approaches unity for Q!1. At nonzero temperatures, it is inadequate to measure the fraction of persistent spins by the number of spins which never ipped until time t: in the presence of thermal uctuations, this quantity decays exponentially fast. Derrida 6 has extended the concept of persistent spins to nonzero temperatures below T C by comparing a system A where coarsening takes place when starting from a random initial conng-uration to a system B which starts with all spins having the same color 1. When submitting both systems to the same thermal noise, it is possible to distinguish thermal uctuations from motions of interfaces in the coarsening process, since the spin ips in system B can be attributed to thermal uctuations. The fraction r(t) Permanent address.