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Critical properties of the long-range random models

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Mathematics and Physics of Anderson localization: 50 Years After

In this talk we consider random matrix ensembles and non-linear sigma models characterized by a long-range random hopping. At criticality, eigenstates of such systems are multifractal and the corresponding multifractal dimensions can be calculated analytically in the limit of strong or weak multifractality. Using explicit results for the multifractal dimensions and the level number variance, we discuss critical properties of various models. Among them are universal and non-universal features of the multifractality spectrum and unusual critical behavior of the two-dimensional power-law random matrix model.

This talk is part of the Isaac Newton Institute Seminar Series series.

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