Strong disorder effects on spin and fermion systems in random magnetic fileds

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General Aims :In order to study strong disorder effects, we apply techniques which has been developed in the gauge glass model to spin and/or fern-don systems.Achievements :1 We study random hopping fermions on bipartite lattices, especially paying attention to strong diorder features of the model. We show that the states at the band center, which have been believed to be extended, are localized.2 We study the disordered double-exchange model. Anomalous spin-wave spectrum which has been observed in various experiments have been attracting much current interest. We show that this anomalous behavior in the spin-wave can be understood by impurities in electron systems.At the same tame, we work on renomalization group approach to a nonlinear diffusion equations. The motibation for this work lies in the study of the random hopping fermion models mentioned in 1. We show that the exact renormalization group is especially useful to Cauchy problems for wider class of nonlinear diffusion equations.We also explore an efficient method of computing Hall conductances in quantum Hall effects.