Three-dimensionalq-state Potts model: Monte Carlo study nearq=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 ${\mathit{q}}_{\mathit{c}}$=2.45±0.1. We also find that the free-energy barrier ΔF(q,L)∼(q-${\mathit{q}}_{\mathit{c}}$ ${)}^2$ ${\mathit{L}}^{2.3}$ and conclude that there is no essential singularity in the correlation length or latent heat in contrast to two dimensions.