High-temperature series study of the q-component Potts model in two and three dimensions

High-temperature series for the free energy of the q-component Potts model in the presence of arbitrary external fields are generated to eight order for five lattices and subsequently analysed. In two dimensions the higher critical exponents gamma , gamma 3 are estimated to be 1.42, 3.60 and 1.20, 2.62 for q=3 and 4 respectively. Evidence for the possible divergence of the order parameter fluctuation at the first-order transition point for q>or=5 is presented. In three dimensions the question of the order of the transition is directly investigated in the temperature-order parameter plane and analysis of the series indicates that the transition is of first order for q>or=3.