Theory and Application of Computation in Statistical Physics

该奖项的广泛主题是使用计算和理论工具的组合来理解统计物理中的复杂系统。这项研究包括三个相关部分：随机场伊辛模型；新算法的发展；从计算复杂性的角度分析物理系统。在新的假设和最近的结果的启发下，将使用副本交换，即并行回火算法，推重标记算法来寻找基态，以及实空间重整化群技术来研究随机场伊辛模型的相变。其目的是了解相变的本质，特别是比热中的奇点。将考虑长程相关孔隙空间中的相变，例如气凝胶。这项工作可能会回答一些长期存在的关于猝灭无序情况下相变的理论问题。随机场伊辛模型被认为描述了吸附在多孔材料中的流体中的相变，这项研究的结果将对化学物理和化学工程产生影响。为了推进自旋系统的计算研究，计划在算法的开发和分析上进行研究，重点是副本交换和集群方法。副本交换方法是研究具有竞争相互作用的复杂系统的最强大的工具之一。开发这类算法的重要性超出了目前的研究，可能与从蛋白质折叠到组合优化的一系列问题有关。除了为随机场伊辛模型的研究提供算法支持外，本研究的目标之一是开发动力学问题的集群算法。第三个主题是研究统计物理中模拟系统的并行计算复杂性。高效的并行算法将被构造并分析用于各种系统，包括扩散、有限聚集和增长网络。根据从检查各种模型中获得的见解，将寻求与结构属性和并行计算复杂性相关的一般结果。例如，有人推测，在相对不受限制的条件下，长程相关性的缺乏意味着快速并行采样算法的存在。对理论计算机科学和统计物理的研究有可能在这两个领域产生深刻的见解。计算复杂性提供了一种稳健的、正式的方法来衡量统计物理学中的历史依赖性，并将加深我们对物理复杂系统如何以及为什么有时会从简单的规则和随机性中出现的理解。除了与研究相关的通常更广泛的影响外，这个项目将让本科生参与计算机模拟，特别是在第三个主题领域。该奖项的广泛主题是使用计算和理论工具的组合来理解统计物理中的复杂系统。这项研究有三个相关的组成部分：随机场伊辛模型；新算法的发展；以及从计算复杂性的角度分析物理系统。这项研究计划特别有趣的是，这项工作处于统计物理学和理论计算机科学的交界处。最近有许多例子表明，统计物理学对计算机科学做出了贡献。这项研究将继续关注这一肥沃的界面。从事这些项目的学生将处于有利地位，为凝聚态物理和计算科学做出贡献。

The broad theme of this award is to understand complex systems in statistical physics using a combination of computational and theoretical tools. The research has three related components: the random field Ising model; the development of new algorithms; and, the analysis of physical systems from the standpoint of computational complexity.Informed by new hypotheses and recent results, the phase transition of the random field Ising model will be studied using a replica exchange, i.e., parallel tempering, algorithm, a push-relabel algorithm, to find ground states, and real-space renormalization group techniques. The objective is to understand the nature of phase transition and particularly the singularities in the specific heat. Phase transitions in long-ranged correlated pore spaces, e.g., aerogels, will be considered. This work will potentially answer some long-standing theoretical questions concerning phase transitions in the presence of quenched disorder. The random field Ising model is believed to describe the phase transitions in fluids absorbed in porous materials and the results of this research should impact chemical physics and chemical engineering. In order to advance computational studies of spin systems, research is planned on the development and analysis of algorithms with an emphasis on replica exchange and cluster methods. Replica exchange methods are among the most powerful tools available for studying complex systems with competing interactions. Developing this class of algorithms has an importance that goes beyond the present study and may be relevant to problems ranging from protein folding to combinatorial optimization. In addition to providing algorithmic support for the random field Ising model study, one goal of this research is to develop cluster algorithms for dynamical problems.The third topic is a study of the parallel computational complexity of simulating systems in statistical physics. Efficient parallel algorithms will be constructed and analyzed for various systems including diffusion limited aggregation and growing networks. Based on insights gained from examining various models, general results will be sought relating structural properties and parallel computational complexity. For example, it is conjectured that, under relatively unrestrictive conditions, the absence of long-range correlations implies the existence of a fast parallel sampling algorithm. Investigations at the interface of theoretical computer science and statistical physics have the potential for yielding profound insights in both fields. Computational complexity provides a robust, formal way to measure history dependence in statistical physics and will sharpen our understanding of how and why physically complex systems sometimes emerge from simple rules and randomness.Besides the usual broader impacts associated with the research, this project will involve undergraduate physics students in computer simulations, especially in the third topical area. %%%The broad theme of this award is to understand complex systems in statistical physics using a combination of computational and theoretical tools. The research has three related components: the random field Ising model; the development of new algorithms; and, the analysis of physical systems from the standpoint of computational complexity.What is particularly interesting about this research program is that the work is at the interface between statistical physics and theoretical computer science. There have been a number of recent examples where statistical physics has contributed to computer science. This research will continue to focus on this fertile interface. Students working on these projects will be well positioned to contribute to both condensed matter physics and computational science.***