Computational Studies of Equilibrium and Non-Equilibrium Phase Diagrams and Critical Properties of Two Physical and Chemical Model Systems with Both Short-Range and Long-Range Interactions or Reactivities

In this dissertation, we introduce long-range interactions into one equilibrium model (Ising model) and one non-equilibrium system (Ziff-Gulari-Barshad model), and study their phase diagrams and critical properties. A new approach to do Wang-Landau simulation: macroscopically constrained Wang-Landau, is proposed in connection with the former system. Our macroscopically constrained Wang-Landau method breaks a multidimensional random walk process in phase space into many separate, one-dimensional random walk processes in the energy space. Each of these random walks is constrained to a different value of the macroscopic order parameters. By knowing the distribution of these constrained variables, we can deduce the multi-variable density of states. When the multi-variable density of states for one set of external parameters is obtained, the density of states at any point in the phase diagram can be obtained by simple transformations. After that, all thermodynamic quantities can be obtained. We apply this method to an antiferromagnetic Ising model with a ferromagnetic long-range interaction. The addition of the long-range interaction induces metastable regions in the phase diagram, and a mean-field class critical point emerges for sufficiently strong long-range interaction. We demonstrate how to use the multi-variable density of states obtained to sketch out the complicated phase diagrams for different values of the long-range interaction. We also give free-energy plots, and plots of the distributions of the order parameters of the system for different special points in these phase diagrams. The Ziff-Gulari-Barshad (ZGB) model, a simplified description of the oxidation of carbon monoxide (CO) on a catalyst surface, is widely used to study properties of nonequilibrium phase transitions. Instead of restricting the CO and atomic oxygen (O) to react to form carbon dioxide (CO₂) only when they are adsorbed in close proximity, we consider a modified model that includes an adjustable probability for adsorbed CO and O atoms located far apart on the lattice to react. We employ large-scale Monte Carlo simulations to study the critical properties of this system. We find that the nonequilibrium critical point changes from the two-dimensional Ising universality class to the mean-field universality class upon introducing even a weak long-range reactivity mechanism.