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.

The Wang-Landau method is used to study thermodynamic properties of a three-dimensional flexible homopolymer chain with continuous monomer positions. Results describing the coil-globule and solid-liquid transitions are presented for chain lengths up to N = 100. In order to elucidate the thermodynamic behavior, finite chain length effects and the influence of the energy range over which the density of states is determined are carefully analyzed. Simulation efficiency is also studied and it is shown that setting the natural logarithm of the final modification factor equal to 10-6 is an appropriate choice for this model.

Large scale Monte Carlo simulations have been used to study long-time domain growth behavior in a compressible, two-dimensional Ising model undergoing phase separation. The system is quenched below the transition temperature from a random spin state, and we investigated the late-time domain size growth law, R(t) = A + Bt n. For "lattice mismatched" systems, we found n = 0.224 ± 0.004 which deviates significantly from the Lifshitz-Slyozov value of n = 1/3 for late-time growth . For a compressible model with no mismatch, we find only a slight deviation from n = 1/3. These results strongly suggest that we do not yet fully understand domain growth.

We present preliminary results for Monte Carlo simulations of a three dimensional semi-flexible polymer chain with continuous monomer positions. In these simulations, standard Metropolis Monte Carlo methods are used to examine the basic properties of the model, such as equilibration configurations, overall size, and transition temperatures.

In this work we study the thermodynamic properties of ultrathin ferromagnetic dots using Monte Carlo simulations. We investigate the vortex density as a function of the temperature and the vortex structure in monolayer dots with perpendicular anisotropy and long-range dipole interaction. The interplay between these two terms in the hamiltonian leads to an interesting behavior of the thermodynamic quantities as well as the vortex density.

Monte Carlo simulations have begun to illuminate the nature of phase transitions and universality classes for compressible Ising models. A comprehensive analysis of a Landau-Ginsburg Wilson hamiltonian for systems with elastic degrees of freedom predicts that there should be four cases with different behavior, depending upon symmetries and thermodynamic constraints. We shall describe the results of careful Monte Carlo simulations for a simple compressible Ising model that can be easily modified to correspond to each of the four cases.

We describe a new algorithm that approaches Monte Carlo simulation in statistical physics in a different way. Instead of sampling the probability distribution at a fixed temperature, a random walk is performed in energy space to directly extract an estimate for the density of states. The canonical probability can then be found at any temperature by weighting by the appropriate Boltzmann factor, and thermodynamic properties can be determined from suitable derivatives of the partition function.

Computer simulations have played an important role in the elucidation of wetting and interface unbinding phenomena. In particular, use of the Ising-lattice-gas model in a film geometry and subject to diverse surface and bulk magnetic fields has permitted extensive Monte Carlo simulations to reveal new features of the phase diagrams associated with these phenomena and to provoke new theoretical studies. The status of our knowledge about the nature of wetting and interface-delocalization transitions which has resulted from these Ising model simulations will be summarized.