Mathematical Studies of Short-Range Spin Glasses In and Out of Equilibrium

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This project addresses a number of basic questions concerning the low temperature behavior of short-range spin glasses and other models of materials with quenched disorder. Rigorous and heuristic mathematical methods will be applied to analyze the multiplicity, structure and organization of pure phases and ground states; non-equilibrium dynamics; and the presence or absence of a thermodynamic phase transition. The relations between spin glasses and problems in combinatorial optimization, biology, and other areas will also be investigated.This award will support the development of mathematical techniques to be applied to investigations of an important class of magnetic materials known as spin glasses. Understanding their behavior is essential to filling a gap in our knowledge of how materials behave when their structure is dominated by randomness and disorder. The techniques developed will also have potential applications to a wide range of complex problems in other areas, such as computer science and biology. Examples of such problems are route scheduling of airlines and predicting the geometric structure (and hence biological function) of proteins. Some of the research done under this award will be carried out by Ph.D. students as a central part of their graduate training.