Theory of Phase Transitions in Quantum and Disordered Systems

研究将在诸如自旋玻璃等受挫系统中进行相变。除了研究自旋玻璃问题的一些方面外，还将探讨将自旋玻璃思想应用于具有磁场无序的II型超导体中漩涡玻璃的存在问题。这将决定高温超导体在磁场中是否具有严格的零电阻。量子系统相变的研究也将得到发展。特别地，我们将研究无序薄膜在绝缘相和超导相之间的零温度转变时的通用电导。由于分析方法对于所提出的问题来说非常复杂，因此重点将放在数值模拟上。数值技术将应用于研究在量子效应和无序占主导地位的各种系统中的相变。包括高温超导体中的自旋玻璃、涡旋玻璃和零温度下无序薄膜中的绝缘体-超导体转变的研究。所有这些问题都是当前凝聚态和材料物理学中非常感兴趣的问题。

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.