Statistical properties of a localization–delocalization transition induced by correlated disorder

The exact probability distributions of the resistance, the conductance and the transmission are calculated for the one-dimensional Anderson model with long-range correlated off-diagonal disorder at E = 0. It is proved that despite the Anderson transition in 3D, the functional forms of the resistance and its related variables distribution functions do not vary when there exists a metal–insulator transition induced by a correlation among disorders. Furthermore, we derive analytically all statistical moments of the resistance, the transmission and the Lyapunov exponent. The rate of growth of the resistance with the length decreases as the Hurst exponent H tends to its critical value (H_cr = 1/2) from the insulating regime. In the metallic regime H ≥ 1/2, all distributions become independent of size. Therefore, in the thermodynamic limit, the resistance and the transmission fluctuations do not diverge with the length in this regime.