Research will be conducted on phase transitions in frustrated systems such as spin glasses. In addition to studying a number of aspects of the spin glass problem, application of spin glass ideas to the issue of the existence of a vortex glass in a type II superconductor with disorder in a magnetic field will also be pursued. This will determine whether high temperature superconductors have strictly zero resistance in a magnetic field. Work on phase transitions in quantum systems will also be developed. In particular, the universal conductance expected at the zero temperature transition between insulating and superconducting phases in disordered thin films will be investigated. Since analytic approaches have turned out to be very complicated for the proposed problems, the emphasis will be on numerical simulations. %%% Numerical techniques will be applied to study phase transitions in a variety of systems in which quantum effects and disorder dominate. Included will be studies of spin glasses, vortex glasses in high temperature superconductors and the insulator- superconductor transition in disordered thin films at zero temperature. All of these problems are of great current interest in condensed matter and materials physics.
