J. Phys. I France 4 (1994) 655-673
Statistical properties of one-point Green functions in disordered systems and critical behavior near the Anderson transitionAlexander D. Mirlin1 and Yan V. Fyodorov2
1 Institut für Theorie der Kondensierten Materie, Universitât Karlsruhe, 76128 Karlsruhe, Germany
2 Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot 76100, Israel
(Received 1 Octoher 1993, accepted 9 Fehruary 1994)
We investigate the statistics of local Green functions , in particular of the local density of states , with the Hamiltonian describing the motion of a quantum particle in a d-dimensional disordered system. Corresponding distributions are related to a function which plays the role of an order parameter for the Anderson metal-insulator transition. When the system can be described by a nonlinear -model, the distribution is shown to possess a specific "inversion" symmetry. We present an analysis of the critical behavior near the mobility edge that follows from the abovementioned relations. We explain the origin of the non-power-like critical behavior obtained earlier for effectively infinite-dimensional models. For any finite dimension the critical behavior is demonstraied to be of the conventional power-law type wilh playing the rote of an upper critical dimension.
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