Topics in lattice gauge theories and spin systems

Several aspects of lattice quantum field theories are explored. The phase diagrams of lattice gauge theories coupled to scalar (Higgs) fields are studied. It is shown that the Higgs and confining regimes are smoothly connected when the Higgs fields are in the fundamental representation. The implementation of a block spin renormalization group for the two-dimensional classical Heisenberg model using Monte Carlo techniques is discussed. Finally, some applications of gauge symmetry to disordered magnetic systems are displayed. The utility of duality transformation is emphasized