Algorithms, States, and Dynamics in Models of Disordered Matter

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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.