Potts models: Density of states and mass gap from Monte Carlo calculations

Monte Carlo simulations are performed for first-order phase-transition models. The three-dimensional three-state Potts model has a weak first-order transition. For this model we calculate the density of states on L³ block lattices (L up to size 36) and obtain high-precision estimates for the leading partition-function zeros. The finite-size-scaling analysis of the first zero exhibits the expected convergence of the critical exponent {ν} toward 1/D for large L; in particular, we find {ν}=2.955(26) from our two largest lattices. Analysis of our specific-heat Cᵥ data yields l=0.080 31(26) for the latent heat. Along another line of approach, we calculate the mass gap m=1/{ξ} ({ξ} is the correlation length) for cylindrical L²{L}z$ lattices (L up to 24 and ${L}z$=256). The finite size-scaling analysis of these results is also consistent with the convergence of {ν} toward 1/D, but that the limiting value is 1/D is not yet conclusively established. Some theoretical arguments favor {ν}{→}0 in case of a first-order transition in a cylindrical L^D-1{∞} geometry. Therefore, we also applied our approach to the 2D ten-state Potts model, which is known to have a strong first-order transition. In this case we find unambiguous evidence in favor of 1/D as the limiting value.