Theory of Phase Transitions in Quantum and Disordered Systems

将对自旋玻璃等受挫系统的相变进行研究。除了研究自旋玻璃问题的许多方面外，还将探讨将自旋玻璃思想应用于在磁场中具有无序的第二类超导体中是否存在涡旋玻璃的问题。这将决定高温超导体在磁场中是否具有严格的零电阻。还将开展量子系统相变方面的工作。特别是，我们将研究无序薄膜中绝缘相和超导相之间零温转变时的普适电导。由于分析方法对于所提出的问题已被证明是非常复杂的，因此重点将放在数值模拟上。数值技术将应用于研究以量子效应和无序为主的各种系统中的相变。包括自旋玻璃、高温超导体中的涡旋玻璃以及零温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物理和材料物理学非常感兴趣的问题。

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.