Phase structure of an SU(2) lattice gauge theory with fundamental Higgs fields

The phase structure of an SU(2) Lattice Gauge Theory which interacts with Higgs fields transforming under the fundamental representation of the gauge group is obtained with mean field and Monte Carlo methods. If the Higgs self coupling, lambda, is large this theory exhibits a second order phase transition for large values of the inverse gauge coupling, β, which does not, however, divide the parameter space into disjoint phases. As the lambda decreases this transition extends to the β = 0 edge parameter space and becomes first order for part of its length. The finite temperature behavior of the theory is also examined. The phase transition line identified in the zero temperature case appears to be a temperature independent feature of the model. However, study of the Wilson line operator indicates that there is a deconfining transition present in the Higgs symmetric phase of the theory which scales according to the gauge coupling renormalization group equation