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 (Tc,Hc), which must be located in a two-dimensional parameter space. The critical field Hc(Q) is positive and increases with Q, in qualitative agreement with previous theoretical predictions.

We use the Wang-Landau algorithm to calculate a density of states for 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 determine the phase diagram and to study the critical behavior of this model at and near the critical endpoint. We observe a divergence of the curvature of the spectator phase boundary at the critical endpoint in accordance with theoretical predictions.

We review recently developed decomposition algorithms for molecular dynamics and spin dynamics simulations of many-body systems. These methods are time reversible, symplectic, and the error in the total energy thus generated is bounded. In general, these techniques are accurate for much larger time steps than more standard integration methods. Illustrations of decomposition algorithms performance are shown for spin dynamics simulations of a Heisenberg ferromagnet.

Fourth-order cumulants of physical quantities have been used to characterize the nature of a phase transition. In this paper we report some Monte Carlo simulations to illustrate the behavior of fourth-order cumulants of magnetization and energy across second and first-order transitions in the phase diagram of a well know spin-1 Ising model. Simple ideas from the theory of thermodynamic fluctuations are used to account for the behavior of these cumulants.