Numerical Studies of Phase Transitions in Disorderd Systems

无序系统相变的数值研究

• 批准号: 0086287
• 负责人: Allan Peter Young
• 金额: $ 30万
• 依托单位: University of California-Santa Cruz
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2000
• 资助国家: 美国
• 起止时间: 2000-11-01 至 2004-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0086287&HistoricalAwards=false
• 关键词: Numerical; Studies; Phase; Transitions; Disorderd

0086287YoungThis grant supports theoretical research on phase transitions in disordered systems. The work is primarily numerical. The research will focus on two areas. The first is to investigate the nature of the spin glass state, which occurs in systems with frustration and disorder. Although the terminology refers to a class of magnetic systems, the concepts developed in spin glasses have a much wider applicability and have found use in other areas of science such as protein folding and optimization problems. Only limited results have been obtained analytically, so numerical simulations have played an important role. Past work has established fairly conclusively that a finite temperature transition does occur. The nature of the spin glass state below the transition temperature is, however, fairly controversial.Recently the PI's group has embarked on a series of studies to elucidate the nature of the spin glass state by investigating how the ground state changes when various types of perturbations are applied. Because of frustration, determination of the ground state is non-trivial and required a fairly sophisticated genetic algorithm. These calculations suggest a picture of the spin glass which is a modified version of one of the proposed theories, the droplet picture, but also contains an important ingredient of the alternative theory, replica symmetry breaking. During the course of this grant, the PI will investigate this scenario in more detail, and, most importantly, check that it is also consistent with finite temperature Monte Carlo simulations on rather small sizes but taken down to temperatures much lower than before using the exchange Monte Carlo method, which considerably reduces the slowing down that occurs at low temperature in conventional Monte Carlo.Since numerical results on spin glasses can only be done on rather small systems at low temperatures, because of long relaxation times due to the many-valley nature of the phase space (which is only partially reduced by the exchange Monte Carlo method), a major concern in the interpretation of numerical data is the size of the corrections to scaling. The PI therefore also intends to look systematically at how the size of these corrections varies for different models, to see if there is an optimal model for which the corrections are smallest.Finally, the second area that will be studied concerns quantum phase transitions with disorder. These are poorly understood compared with classical phase transitions at finite temperature. This is because many of the techniques used successfully in classical transitions don't work in the quantum case, perhaps because non-perturbative (Griffiths-McCoy) effects are important. Hence again, numerical work has been very important. Several studies will be carried out.%%%This grant supports theoretical research on phase transitions in disordered systems. The work is primarily numerical. The research will focus on two areas. The first is to investigate the nature of the spin glass state, which occurs in systems with frustration and disorder. Although the terminology refers to a class of magnetic systems, the concepts developed in spin glasses have a much wider applicability and have found use in other areas of science such as protein folding and optimization problems. Only limited results have been obtained analytically, so numerical simulations have played an important role.The second area that will be studied concerns quantum phase transitions with disorder. These are poorly understood compared with classical phase transitions at finite temperature. This is because many of the techniques used successfully in classical transitions don't work in the quantum case, perhaps because non-perturbative (Griffiths-McCoy) effects are important. Hence again, numerical work has been very important. Several studies will be carried out.***

0086287 young本基金支持对无序系统相变的理论研究。这项工作主要是数字方面的。研究将集中在两个方面。首先是研究自旋玻璃态的性质，它发生在具有挫折和无序的系统中。虽然这个术语指的是一类磁系统，但自旋玻璃中发展的概念具有更广泛的适用性，并已在其他科学领域（如蛋白质折叠和优化问题）中得到应用。解析得到的结果有限，因此数值模拟发挥了重要作用。过去的工作已经相当确凿地证实，有限的温度转变确实会发生。然而，低于转变温度的自旋玻璃态的性质是相当有争议的。最近，PI的团队已经开始了一系列的研究，通过研究在不同类型的扰动作用下基态是如何变化的，来阐明自旋玻璃态的本质。由于挫折，确定基态是不平凡的，需要一个相当复杂的遗传算法。这些计算提出了一个自旋玻璃的图像，它是提出的理论之一，液滴图像的修改版本，但也包含了另一种理论的重要组成部分，即复制对称破缺。在这项资助的过程中，PI将更详细地研究这种情况，最重要的是，检查它是否与有限温度蒙特卡罗模拟在相当小的尺寸上是一致的，但温度比使用交换蒙特卡罗方法之前低得多，这大大减少了传统蒙特卡罗在低温下发生的减速。由于自旋玻璃的数值结果只能在相当小的系统中在低温下完成，因为相空间的多谷性质导致了长松弛时间（仅部分通过交换蒙特卡罗方法减少），因此在解释数值数据时主要关注的是缩放修正的大小。因此，PI还打算系统地研究这些修正的大小在不同模型中是如何变化的，看看是否存在一个修正最小的最佳模型。最后，第二个将被研究的领域涉及无序的量子相变。与有限温度下的经典相变相比，人们对这些相变知之甚少。这是因为许多在经典跃迁中成功使用的技术在量子情况下不起作用，也许是因为非微扰（格里菲斯-麦考伊）效应很重要。因此，数值工作是非常重要的。将进行几项研究。该基金支持对无序系统相变的理论研究。这项工作主要是数字方面的。研究将集中在两个方面。首先是研究自旋玻璃态的性质，它发生在具有挫折和无序的系统中。虽然这个术语指的是一类磁系统，但自旋玻璃中发展的概念具有更广泛的适用性，并已在其他科学领域（如蛋白质折叠和优化问题）中得到应用。解析得到的结果有限，因此数值模拟发挥了重要作用。第二个要研究的领域涉及无序的量子相变。与有限温度下的经典相变相比，人们对这些相变知之甚少。这是因为许多在经典跃迁中成功使用的技术在量子情况下不起作用，也许是因为非微扰（格里菲斯-麦考伊）效应很重要。因此，数值工作是非常重要的。将进行几项研究