The two- and three-dimensional q-state Potts model is simulated by a c
luster algorithm and the relaxation dynamics of average cluster size a
nd the order parameter during initial thermalization are studied. The
dependence of these quantities on the lattice size and Ci in the early
stages of Monte Carlo iterations reveals valuable information on the
nature of the phase transition occurring in the system. From the initi
al thermalization data of the 2D 7-state Potts model, surface tension
is also calculated. The value is in good agreement with the exact resu
lt. (C) 1998 Elsevier Science B.V. All rights reserved.