A new class of disordered systems a modified Bernoulli system with long range structural correlation

Spectral property and Lyapunov exponent of electronic wave function (L-exponent) in a modified Bernoulli system with inverse-power-law structural correlation, is studied in detail numerically and theoretically. By changing the value of the bifurcation parameter B specifying a strength of the correlation in the interval (1, ∞), two transitions (a transition around B = 3/2 and another one at B = 2) appear. For the case 3/2 ≤ B <2 of long-range structural correlation, two peaks appear and compete in the distribution function of L-exponent of finite system and the distribution does not obey the central-limit theorem. At the critical point B = 2 (and also for B>2), Lexponent in infinite system vanishes with probability 1.