Theory and Application of Computation in Statistical Physics

该奖项的主要主题是利用计算和理论工具的结合来理解统计物理中的复杂系统。该研究有三个相关组成部分：随机场Ising模型；新算法的开发；从计算复杂性的角度分析物理系统。根据新的假设和最近的结果，将使用副本交换，即并行回火，算法，推-重新标记算法，寻找基态和实空间重整化群技术来研究随机场Ising模型的相变。目的是了解相变的性质，特别是比热的奇点。将考虑长期相关孔隙空间（例如气凝胶）中的相变。这项工作将有可能回答一些长期存在的理论问题，有关相变在淬火无序的存在。随机场Ising模型被认为可以描述多孔材料中吸收的流体的相变，本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，计划对算法的开发和分析进行研究，重点是副本交换和聚类方法。副本交换方法是研究具有相互竞争作用的复杂系统的最强大的工具之一。开发这类算法具有超越当前研究的重要性，并且可能与从蛋白质折叠到组合优化等问题相关。除了为随机场Ising模型研究提供算法支持外，本研究的一个目标是开发动态问题的聚类算法。第三个主题是统计物理中模拟系统并行计算复杂性的研究。本文将构建并分析各种系统的高效并行算法，包括扩散有限聚合和增长网络。基于从检查各种模型中获得的见解，将寻求与结构特性和并行计算复杂性相关的一般结果。例如，据推测，在相对不受限制的条件下，不存在远程相关性意味着存在快速并行采样算法。在理论计算机科学和统计物理学的界面上进行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健壮的、正式的方法来测量统计物理学中的历史依赖性，并将增强我们对物理复杂系统有时如何以及为什么从简单规则和随机性中出现的理解。除了通常与研究相关的更广泛的影响外，该项目将涉及计算机模拟的本科物理学生，特别是在第三主题领域。该奖项的主要主题是利用计算和理论工具的结合来理解统计物理学中的复杂系统。该研究有三个相关组成部分：随机场Ising模型；新算法的开发；从计算复杂性的角度分析物理系统。这个研究项目特别有趣的地方在于，它是统计物理学和理论计算机科学的结合。最近有很多统计物理学对计算机科学做出贡献的例子。这项研究将继续关注这个肥沃的界面。从事这些项目的学生将很好地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.***