Study of phase transitions in spin and gauge models using Fisher's zeros

In this thesis we will discuss spin and gauge models on a lattice and the analysis of these models with the goal of devising optimal methods to treat more complicated gauge models using the same methods. Monte Carlo lattice simulations are the prominent method of studying many physical phenomenon which makes understanding the general behavior of these simulations an important area of study. We will be looking at models that do not require enormous amounts of computer time starting with the 2D Ising spin model, then the 2D O(2) spin model, followed by the 3D U(1) gauge model and finishing with the 4D SU(2) with an adjoint representation gauge model. The SU(2) model is of the most interest to us because it contains features that are seen in more complicated models such as SU(3) with 8 or 12 flavors.

In all of these models we are interested in looking at the nature (order) of the phase transitions, if there is one, and the volume dependence of certain quantities. We are most interested in the phase transition talked about by Michael Creutz and Gyan Bahnot which occurs in the Β, Β adjoint plane and ends before the transition line touches the Β fundamental axis. The point where this line ends has not been fully explored, and is a feature that is found in other gauge models. For example similar lines of bulk or thermal phase transitions occur in models that are now being considered as possible candidates to provide a dynamical alternative to the Higgs mechanism such as SU(3) with 8 or 12 flavors of fundamental quarks.