Phase transitions in lattice gauge theories

Abstract

Topological excitations in lattice gauge theories are studied with an aim towards understanding the role of such excitations in the Abelian Higgs model. First, the topological excitations of the compact U(l) lattice Higgs model are reviewed. The phases of the system are discussed in terms of these excitations and the results of Monte Carlo studies summarized. New results are then presented clarifying the role of topological excitations in the non-compact lattice version of the Abelian Higgs model. The Villain form of the non-compact model's partition function is represented as a sum over world-sheets of gauge-invariant "vortex" sheets. The phase transition of the system is then related to the condensation of these excitations via standard energy-entropy arguments. Results of Monte Carlo simulations are then presented. The density of the vortex sheets is shown to be a good disorder parameter for the system. The vortex density essentially vanishes in the Higgs phase, and the Coulomb phase consists of a single vortex condensate. The critical line derived in the vortex representation of the theory is in good agreement with the Monte Carlo results. In part II Quantum Chromo dynamics ( QCD) is studied at non-zero baryon density. The essential properties of QCD are reviewed, including the broken chiral symmetry of the QCD vacuum state. The current understanding of the deconfining and chiral symmetry restoring transitions at non-zero temperature and density is then summarized. The use of a four-fermion coupling as an improved extrapolation parameter over the bare quark mass in Monte Carlo simulations is discussed. A mean field analysis of finite density QCD is then presented, including the effects of additional chiral invariant four-fermion interactions. A lattice regularization is used with N1 = 4 flavors of staggered fermions. Particular attention is given to the structure of the phase diagram and the order of the chiral phase transition. At zero gauge coupling the model reduces to a Nambu-Jona-Lasinio model. In this limit the chiral phase transition is found to be second-order near the zero-density critical point and otherwise first-order. In the strong gauge coupling limit a first-order chiral phase transition is found. In this limit the additional four-fermion interactions do not qualitatively change the physics. The results agree with previous studies of QCD as the four-fermion coupling vanishes.U of I OnlyThesi