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Title:  Phase transitions in lattice gauge theories 
Author(s):  Chavel, Michael V. 
Doctoral Committee Chair(s):  Kogut, John B. 
Department / Program:  Physics 
Discipline:  Physics 
Degree:  Ph.D. 
Genre:  Dissertation 
Subject(s):  phase transitions
lattice gauge theories Abelian Higgs model Quantum Chromo dynamics 
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 noncompact lattice version of the Abelian Higgs model. The Villain form of the noncompact model's partition function is represented as a sum over worldsheets of gaugeinvariant "vortex" sheets. The phase transition of the system is then related to the condensation of these excitations via standard energyentropy 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 nonzero 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 nonzero temperature and density is then summarized. The use of a fourfermion 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 fourfermion 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 NambuJonaLasinio model. In this limit the chiral phase transition is found to be secondorder near the zerodensity critical point and otherwise firstorder. In the strong gauge coupling limit a firstorder chiral phase transition is found. In this limit the additional fourfermion interactions do not qualitatively change the physics. The results agree with previous studies of QCD as the fourfermion coupling vanishes. 
Issue Date:  1997 
Genre:  Dissertation / Thesis 
Type:  Text 
Language:  English 
URI:  http://hdl.handle.net/2142/30774 
Other Identifier(s):  4039258 
Rights Information:  ©1997 Chavel 
Date Available in IDEALS:  20120426 
This item appears in the following Collection(s)

Graduate Dissertations and Theses at Illinois
Graduate Theses and Dissertations at Illinois 
Dissertations and Theses  Physics
Dissertations in Physics