Phase Transitions Critical Phenomena and Disordered System

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Theoretical research will be conducted on quantum spin glasses, the finite connectivity spin glass and on self-organizing critical phenomena. For quantum spin glasses investigations will be made of the quantum Heisenberg spin glass in a field, the Potts spin glass in a transverse field and the quantum spin glass on finite connectivity lattices. For the finite connectivity spin glass we will look at static and dynamic properties, patterns of replica symmetry breaking and their stability, behavior of correlation functions and fluctuations, as a step toward understanding the short range model. We will include small loops as a means to go beyond the Bethe approximation toward behavior on a Bravais lattice. We will also look at field theoretical models corresponding to non-equilibrium stationary states displaying self- organized criticality for which cellular automata exist and at dynamical behavior of systems driven by an external field near their critical point.