Uncovering the secrets of unusual phase diagrams: Applications of two-dimensional Wang-Landau sampling

We use a two-dimensional Wang-Landau sampling algorithm to calculate the density of states for two discrete spin models and then extract their phase diagrams. The first system is an asymmetric Ising model on a triangular lattice with two- and three-body interactions in an external field. An accurate density of states allows us to locate the critical endpoint accurately in a two-dimensional parameter space. We observe a divergence of the spectator phase boundary and of the temperature derivative of the magnetization coexistence diameter at the critical endpoint in quantitative agreement with theoretical predictions. The second model is a Q-state Potts model in an external field H. We map the phase diagram of this model for Q >= 8 and observe a first-order phase transition line that starts at the H = 0 phase transition point and ends at a critical point (T-c,H-c), which must be located in a two-dimensional parameter space. The critical field H-c(Q) is positive and increases with Q, in qualitative agreement with previous theoretical predictions.