Computational Studies of Complex and Frustrated Systems

该奖项支持统计物理和凝聚态物理的理论和计算研究，组织在三个相关项目中。1. PI将开发算法来模拟受挫自旋系统和具有粗糙自由能景观的相关系统。PI旨在改进并行回火算法和种群退火算法。2. PI将对伊辛自旋玻璃模型进行大规模的计算研究。本研究的主要目标是解决关于在有限维系统中，自旋玻璃有序是在只有两个热力学纯态的液滴图像中以简单的方式发生，还是通过涉及大量纯态的更复杂的复制对称破缺场景发生的争议。在这项研究中，PI和合作者将对伊辛自旋玻璃进行大规模模拟，并使用新的观测数据分析重叠分布的统计数据，这些观测数据可以明显区分这些场景。用平行回火和群体退火来研究硬物体的堆积问题。3. 最后一个领域涉及并行计算复杂性理论在统计物理问题中的应用。并行计算复杂性理论中的p完备性概念将扩展到抽样问题，并应用于证明扩散有限聚集等增长模型是固有序列的。这项工作扩展并建立在早期结果的基础上，这些结果表明扩散有限聚集和统计物理中的其他过程是p完全的。该项目非常重视教育，大部分预算用于支持研究生和本科生，他们将接受统计、凝聚态物质和计算物理的概念和技术培训。该奖项支持统计和凝聚态物理的理论研究和教育。该研究由几个相关的项目组成，这些项目涉及跨学科边界的计算和概念。PI的目标是开发计算机算法，以克服材料的计算挑战，这些材料在许多可能性中表现出挫折或障碍，无法找到真正的解决方案，例如蛋白质的折叠结构。这类问题不仅在物理科学中很重要，而且在计算机科学和工程中也很重要，它们被称为组合优化问题。旋转眼镜就是一个令人沮丧的例子。它们是磁性材料，在这些材料中的原子尺度磁性成分之间具有随机相互作用，这些成分通常被称为自旋。随机的相互作用导致“挫折”自旋从不同的邻居那里接收到相互冲突的信号，关于它们应该如何定位自己。由于受挫，旋转玻璃需要很长时间才能达到平衡。对于自旋玻璃模型的计算机模拟也是如此；它们需要很长的计算时间。PI的目标是开发能够克服模拟受挫系统的挑战的计算机算法。这些算法将被用于对自旋玻璃进行大规模的计算研究，这将有助于解决无序材料理论中一个长期存在的基本争议。PI将能够在较低的温度下进行比目前可能的更广泛的模拟，并利用新的技术，可以更清楚地区分许多平衡状态或单个状态对的存在。PI还试图了解在具有并行处理器的计算机上模拟材料系统的计算难度是否与物理系统有基本的联系。PI将研究扩散有限聚集，这是一种描述矿物沉积和雪花生长的生长过程，并产生复杂的图案。问题是，从这个过程中产生的模式是否可以由并行计算机快速生成，或者模式形成过程本身是否基本上是顺序的，并且不可并行化。这些结果可以指导理解计算机上的并行化是否会导致特定问题的更高性能，以及测量材料或其他物理系统固有复杂性的新方法。该项目非常重视教育，大部分预算用于支持研究生和本科生，他们将接受统计、凝聚态物质和计算物理的概念和技术培训。

TECHNICAL SUMMARYThis award supports theoretical and computational research in statistical physics and condensed matter physics organized in three related projects. 1. The PI will develop algorithms for simulating frustrated spin systems and related systems with rough free energy landscapes. The PI aims to improve both the parallel tempering and the population annealing algorithms. 2. The PI will carry out a large-scale computational study of Ising spin glass models. The primary goal of this research is to resolve the controversy over whether, in finite-dimensional systems, spin glass ordering occurs in the simple way as proposed in the droplet picture with only two thermodynamically pure states or through the more complex replica symmetry breaking scenario involving a large multiplicity of pure states. In this study, the PI and collaborators will carry out large scale simulations of Ising spin glasses and analyze the statistics of the overlap distribution using new observables that sharply distinguish these scenarios. The problem of packing hard objects will also be studied using both parallel tempering and population annealing. 3. The last area involves the application of the theory of parallel computational complexity to problems in statistical physics. The notion of P-completeness in parallel computational complexity theory will be extended to sampling problems and applied to prove that growth models such as diffusion limited aggregation are inherently sequential. This work extends and builds on early results that show that diffusion limited aggregation and other processes in statistical physics are P-complete. This project has a significant emphasis on education and much of the budget is devoted to supporting graduate and undergraduate students who will be trained in the concepts and techniques of statistical, condensed matter, and computational physics. NON-TECHNICAL SUMMARYThis award supports theoretical research and education in statistical and condensed matter physics. The research consists of several related projects that involve computation and concepts that cross disciplinary boundaries.The PI aims to develop computer algorithms that can overcome the computational challenges of materials that exhibit frustration or barriers to finding the true solution among many possibilities, such as the folded structure of a protein. This general class of problems is important not only in the physical sciences but also in computer science and engineering where they are called combinatorial optimization problems. Spin glasses provide an example of frustration. They are magnetic materials with random interactions between the atomic scale magnetic constituents in these materials often referred to as spins. The random interactions lead to "frustration" spins receive conflicting signals from different neighbors as to which way they should orient themselves. Due to frustration spin glasses take a very long time to reach equilibrium. This is also true for computer simulations of models of spin glasses; they require very long computation times. The PI aims to develop computer algorithms that can overcome the challenges of simulating frustrated systems. The algorithms will then be used to carry out a large scale computational study of spin glasses that will help to resolve a long-standing and fundamental controversy in the theory of disordered materials. The PI will be able to carry out more extensive simulations for lower temperatures than has been possible up to now, and utilize new techniques that can more sharply distinguish between the existence of many equilibrium states or a single pair of states. The PI also seeks to understand whether computational difficulty of simulations of materials systems on computers with processors that can work in parallel has a fundamental connection to the physical system. The PI will study diffusion limited aggregation, a growth process that describes, for example, mineral deposition and snowflake growth, and creates complex patterns. The question is whether patterns that arise from this process can be generated rapidly by a parallel computer or whether the pattern formation process itself is fundamentally sequential one and not parallelizable. These results may guide the understanding of whether parallelization on a computer will lead to higher performance for a particular problem, and a new way to measure the inherent complexity of a material or other physical system.This project has a significant emphasis on education and much of the budget is devoted to supporting graduate and undergraduate students who will be trained in the concepts and techniques of statistical, condensed matter, and computational physics.