Theory of Phase Transitions in Quantum and Disordered Systems

9713977杨这笔赠款支持一名高级国际和平人员的继续工作，他因对统计力学中几个问题的数值分析做出了重大贡献而受到表彰。在目前的拨款中，他计划对随机磁系统中的量子相变进行理论研究。这些问题可以使用复杂、最先进的数值技术来解决。主要目的是：(1)寻找量子相变时的普遍临界行为；(2)研究顺磁相位奇点，称为Griffiths-McCoy奇点。大多数相变是经典的，即相变发生在比量子力学效应在给定系统中变得重要时更高的温度。然而，通过引入无序，转变温度可以降低。考虑到在低温下研究材料性质的简便性，可以想象，新的转变在本质上可能是强烈的量子性质。量子和无序的结合提供了一个既复杂又没有被很好研究的框架。这位资深的PI计划进行一项数值研究，以了解在存在强烈无序的情况下，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. ***