Algorithms, States, and Dynamics in Models of Disordered Matter

非技术总结该奖项支持旨在提高我们对原子随机排列材料的理解的理论和计算研究。这类材料，包括磁性材料、窗玻璃和含有许多杂质的超导材料，都可能受到其内在随机性的强烈影响。无序物质的性质随时间变化极其缓慢。这种缓慢的进化为这些材料提供了显着的复杂性和复杂的记忆，但在计算机上直接模拟效率低下，因为需要极长的模拟时间。PI的团队将寻找新的程序来加速模拟这种缓慢演变的物质。这些程序将被用来探索一大类无序材料的一般性质。PI的小组将研究计算机算法和物理学之间的深层联系。例如，我们每天用来在地图上找到最短路径的算法可以用来找到材料中能量最低的断裂路径。在计算机科学中开发的用于研究复杂网络（例如社会、计算机或交通）的算法在无序物质中有许多应用。作为回报，对物质的物理见解建议改进计算机科学中更广泛适用的算法。该项目的更广泛影响包括培训学生掌握在许多科学和技术领域都有应用的高级计算方法。为每个项目开发的计算机代码将很快提供给其他研究人员不受限制地使用。该项目还旨在加强理论凝聚态物理学、数学物理学和计算机科学之间的联系。技术总结玻璃和复杂的能量景观在凝聚态和软物质物理学中具有广泛的重要性，如结构玻璃、随机磁体、颗粒材料和构造的介观系统，如II型超导体或人工自旋冰中的涡旋通道。该奖项支持凝聚态和统计物理方面的工作，以提高我们对非均匀玻璃材料行为的理解和模拟能力。自旋玻璃合金和其他无序材料模型的数值研究将用于探索一般的玻璃态行为。直接微观动态模拟玻璃模型往往是不可能的，由于大范围的时间尺度，需要覆盖。有效的算法和计算复杂性的连接将进一步发展，为这些具有挑战性的模型系统构建有效的优化和配置采样方法。尺度方法和其他分析将指导计算方法。我们的目标是使用模拟来识别空间变化，使无序材料具有外部参数变化的复杂记忆。更一般地说，这项工作旨在更精确地描述和描述这种记忆和玻璃化的高维景观。这种表征将包括低自由能状态的可控性的调查。例如，本课程将以较低的成本，透过重复穷举法的加速方法，研究有限维模型的内部状态对边界条件的影响。本课程将训练研究生设计及开发电脑程式，以研究复杂的物理系统。这些新代码将依赖于最近开发的复杂算法，并将包括传统上没有教物理学家的一般优化和采样方法。该项目还将侧重于加强凝聚态和统计物理之间的跨学科联系，开发算法和计算机科学基准问题集。这种联系来自于相关的数学结构和所研究的大型复杂系统。学生将接受严格分析和验证大型复杂模拟结果的培训，包括大型数据集。为每个项目开发的代码（例如，二维随机磁体的精确采样算法、可能用于量子蒙特卡罗模拟的平面二聚体模型和随机势中的界面）将免费广泛分发，并附有文档，以促进社区的研究和高级培训。

NON-TECHNICAL SUMMARYThis award supports theoretical and computational research aimed at improving our understanding of materials where atoms are randomly arranged. This class of materials, including magnetic materials, window glass, and superconducting materials with many impurities, can be strongly affected by their built-in randomness. The properties of disordered matter change extremely slowly over time. This slow evolution provides these materials with remarkable complexity and intricate memories, but makes direct simulation on a computer inefficient, as extremely long simulations are needed. The PI's group will search for novel procedures to speed up the simulation of such slowly evolving matter. These procedures will be used to explore the general properties of a wide class of disordered materials.The PI's group will investigate the deep connections between computer algorithms and physics. As an example, algorithms that we use every day to find the shortest route on a map can be used to find the lowest-energy fracture path in a material. Algorithms developed in computer science to study complex networks (social, computer, or transportation, for example) have many applications to disordered matter. In return, physical insights about matter have suggested improvements in more widely applicable algorithms in computer science.The broader impacts of this project include training of students in advanced computational methods that have applications in many scientific and technical domains. Computer codes developed for each project will be quickly made available for unrestricted use by other researchers. This project also aims to strengthen ties between theoretical condensed matter physics, mathematical physics and computer science.TECHNICAL SUMMARYGlassiness and complex energy landscapes are of wide importance in condensed matter and soft matter physics, as seen for structural glasses, random magnets, granular materials, and constructed mesoscopic systems such as vortex channels in type-II superconductors or artificial spin ice. This award supports work in condensed matter and statistical physics to improve both our understanding and our ability to simulate the behavior of inhomogeneous glassy materials. Numeric studies of models of spin glass alloys and other disordered materials will be used to explore general glassy behavior. Direct microscopic dynamic simulations of glassy models are often not possible due to the large range of time scales that need to be covered. Efficient algorithms and connections with computational complexity will be further developed to construct efficient optimization and configuration sampling methods for these challenging model systems. Scaling approaches and other analyses will guide the computational approaches. The goal will be to use simulations to identify the spatial changes that allow disordered materials to have complex memories of external parameter changes. More generally, this work aims to characterize and describe more precisely the high-dimensional landscapes that underlie such memory and glassiness. This characterization will include the investigation of the controllability of the low free energy states. For example, the effects of boundary conditions on the interior state of finite dimensional models will be studied through accelerated methods that replicate exhaustive enumeration with less cost.Graduate students will be trained in design and development of computer codes to study complex physical systems. These new codes will rely on recently developed sophisticated algorithms and will include general optimization and sampling methods that have not traditionally been taught to physicists. This project will also focus on strengthening the interdisciplinary connections between condensed matter and statistical physics with algorithm development and benchmark problem sets for computer science. Such connections result from the related mathematical structures and large complex systems studied. Students will be trained in rigorous analysis and verification of the results of large complex simulations, including large data sets.Codes developed for each project (e.g., exact sampling algorithms for two-dimensional random magnets, planar dimer models as might be used in quantum Monte Carlo simulations, and interfaces in random potentials) will be freely and widely distributed with documentation to facilitate both research by the community and advanced training.