Theory of Phase Transitions in Quantum and Disordered Systems

9713977 Young该基金支持一位资深PI的继续工作，他因对统计力学中几个问题的数值分析作出重大贡献而闻名。在目前的资助下，他计划进行随机磁系统中量子相变的理论研究。这些问题可以用复杂的、最先进的数值技术来解决。主要目标是：(1)寻找量子跃迁的普遍临界行为；(2)研究特征顺磁相位奇点，称为格里菲斯-麦考伊奇点。大多数相变都是经典的，也就是说，与量子力学效应在给定系统中变得重要时相比，相变发生在较高的温度下。然而，可以通过引入无序来降低转变温度。考虑到在低温下研究材料性质的容易程度，可以想象，新的转变可能在本质上是强量子的。量子与无序的结合提供了一个既复杂又未被很好研究的框架。这位高级PI计划进行一项数值研究，以了解在强无序存在的量子相变中会发生什么。* * *

9713977 Young This grant supports the continuing work of a senior PI, distinguished for his significant contributions to the numerical analysis of several problems in statistical mechanics. In the present grant he is planning to conduct theoretical studies of quantum phase transitions in random magnetic systems. These problems can be solved using sophisticated, state-of-the-art numerical techniques. The principal objectives are to: (1) search for universal critical behavior at the quantum transition and (2) to investigate the characteristic paramagnetic phase singularities, called the Griffiths-McCoy singularities. %%% Most phase transitions are classical, i.e. the phase transitions takes place at temperatures which are high compared to when the quantum mechanical effects become important in a given system. And yet, the transition temperatures can be reduced by introduction of disorder. Given the ease in studying material properties at low temperatures, it is conceivable that novel transitions may be strongly quantum in nature. The combination of quantum and disorder provides a framework which is both complex and has not been studied well before. This senior PI plans to carry out a numerical study, to lead to an understanding of what to expect in a quantum phase transition in the presence of strong disorder. ***