Monte Carlo Simulations of Phase Transitions
Phase transitions of diverse kinds occur in an immense variety of physical systems. We use large scale, importance sampling Monte Carlo simulations to carefully examine the equilibrium thermodynamic behavior for different models in statistical physics. Our goal is to elucidate the effects of changing spatial dimensionality, symmetry, and interactions and to search for Universal behavior. We will focus on magnetic phase transitions that occur in simple lattice models, but we also examine order-disorder transitions in semiconductor alloys, equilibrium polymers, interface delocalization, and surface reconstruction. Appropriate models can be constructed that are well suited for simulation and visualization, and these will be investigated from different perspectives. We use standard Monte Carlos sampling techniques as well as novel new methods like Wang-Landau sampling.