Models of Glasses and Spin Glasses

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They propose to gain insights into the behavior of glasses and spin glasses through the development and solution of several model systems. First, they will solve for the cluster effects on the statics and dynamics of spin glasses on the Bethe lattice; they will make rigorous and exact statements about the Griffiths dynamics and the scaling properties of spin glass phase. Second, they will use their elastic-dipole model of the low temperature properties of glasses to answer several theoretical questions: they will investigate the nature of the tunneling centers responsible for the universal properties below 1K and the character and behavior of the harmonic modes responsible for the universal properties from 1K to 50K. Third, they propose to develop a renormalization-group analysis of a model exhibiting an equilibrium liquid - glass phase transition. Finally, they are developing a theory of the non-equilibrium thermodynamics of glasses, valid in the limit of slow cooling rates.