3-DIMENSIONAL Q-STATE POTTS-MODEL - MONTE-CARLO STUDY NEAR Q=3

We provide a convincing numerical demonstration of the first-order nature of the transition in the three-state ferromagnetic Potts model in three dimensions by combining Monte Carlo simulations of the bulk free-energy barrier between the ordered and disordered states with finite-size scaling. From the histogram of internal energy and the number of clusters we extrapolate in q, the number of states, and find q(c) = 2.45 +/- 0.1. We also find that the free-energy barrier DELTA-F(q,L) approximately (q - q(c))2L2.3 and conclude that there is no essential singularity in the correlation length or latent heat in contrast to two dimensions.