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

总体目标：为了研究强无序效应，我们将规范玻璃模型中发展起来的技术应用到自旋和/或fern-don系统中，主要成果如下：1研究了二分格点上的随机跳跃费米子，特别关注了模型的强二序特征。我们表明，在带中心的状态，这一直被认为是扩展的，是本地化的。2我们研究的无序双交换模型。反常自旋波谱在各种实验中被观测到，引起了人们极大的兴趣。我们证明了自旋波中的这种反常行为可以用电子系统中的杂质来理解。同时，我们研究了非线性扩散方程的重整化群方法。本工作的动机在于研究文献[1]中提到的随机跳跃费米子模型。我们证明了精确重整化群对于更广泛的一类非线性扩散方程的Cauchy问题是特别有用的.我们还探索了计算量子霍尔效应中霍尔电导的一种有效方法.

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.