Mathematical Studies of Short-Range Spin Glasses

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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 conjectured presence of a phase transition; the multiplicity, structure and organization of pure phases and ground states; the effect of small magnetic fields; and non-equilibrium dynamics.The purpose of this project is to develop mathematical techniques and results in certain specific models of low temperature materials, known as spin glasses. The importance of the project is that these techniques have potential application to a wide range of problemsarising in areas such as theoretical computer science or biology which combine issues of complexity and optimization. Examples of such problems are optimal route scheduling of airlines and predicting the geometric structure (and hence biological function) of proteins.