Lowe, Anthony Peter (1987) Lattice gauge - Higgs theories. University of Southampton, Doctoral Thesis.
Abstract
We study the phase diagram of lattice regularised gauge theories coupled to fixed-length scalar (Higgs) fields using two techniques: the mean field method and Monte-Carlo simulations. We begin with a review of previous work on the subject paying particular attention to the ways in which the phase diagram is affected by the gauge group and the dimensionality.Next we give a modern presentation of mean field theory as applied to pure gauge theories. We start with a variational approach and then go on to consider the equivalent, but more powerful, saddle-point formulation. We proceed to apply the saddle-point formulation to Z(2) gauge-Higgs theory. The predicted phase diagram turns out to be dependent on the gauge choice but we show that this difficulty is not as serious as it at first appears. We see that certain gauge choices are bound to give trouble. This leads us to the idea of employing covariant gauge fixing. We go on to apply the covariant gauge fixing saddle-point technique to the U(1) Higgs model in three, four and five dimensions. In four dimensions we obtain very good predictions for the phase diagram. However the results for the three dimensional case are not at all satisfactory.Finally we present the results of a Monte-Carlo simulation of the three dimensional U(1) model. We find that there is a line of second order phase transitions connecting the XY model transition at beta= ∞, k = 0.453 to an endpoint in the interior of the phase diagram. This line of transitions has XY model critical exponents. (D76241)
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