Mathematical Sciences: The Mathematics and Physics of Disordered Materials

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The two co-principal investigators will study many problems connected with disordered materials. The physical events to be studied include unfrustrated bond random magnets, disordered electronic systems and spin glasses. Analysis of the corresponding mathematical models is expected to lead to fundamental discoveries about these events such as low temperature properties of spin glasses. The mathematical models used include percolation and classical transport models, and stochastic growth models. Most of the questions relate to the equilibrium properties but some relate to the dynamics. Behavior near the phase transitions will be of particular interest. The novelty of this project is the rigorous study, rooted primarily in mathematics, of systems that are generally studied experimentally. The investigators have already made very valuable contributions to the field including the existence of a spin-glass phase for an Ising model on a Cayley tree.