Short-time dynamics of cluster growth in the Potts model

The two- and three-dimensional q-state Potts model is simulated by a cluster algorithm and the relaxation dynamics of average cluster size and the order parameter during initial thermalization are studied. The dependence of these quantities on the lattice size and q in the early stages of Monte Carlo iterations reveals valuable information on the nature of the phase transition occurring in the system. From the initial thermalization data of the 2D 7-state Potts model, surface tension is also calculated. The value is in good agreement with the exact result.