Abstract

The Anderson localization is investigated for the tight binding model on the 2D square lattice where the phase of each transfer integral is an independent random variable between 0 and 2π. This corresponds to the model of the electronic states in the random magnetic field. We calculate the Thouless number by diagonalizing the Hamiltonian matrix of the square sample and the localization length for the stripe sample by the MacKinnon’s method. We find that the localization length ξ behaves approximately as ξ ∝ exp(14.5E) when the energy E is near the band edge E 0. In the finite energy region around E = 0 any symptom of the localization is not seen up to the width of 64 sites. This suggests the possibility of the existence of the mobility edge in this 2D model.

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