Multifractality of Hamiltonians with power-law transfer terms

Finite-size effects in the generalized fractal dimensions $d_q$ are investigated numerically. We concentrate on a one-dimensional disordered model with long-range random hopping amplitudes in both the strong- and the weak-coupling regime. At the macroscopic limit, a linear dependence of $d_q$ on $q$ is found in both regimes for values of q \alt 4g^{-1}, where $g$ is the coupling constant of the model.Comment: RevTex4, 5 two-column pages, 5 .eps figures, to be published in Phys. Rev.

f(α)f(\alpha) Multifractal spectrum at strong and weak disorder

The system size dependence of the multifractal spectrum $f(\alpha)$ and its singularity strength $\alpha$ is investigated numerically. We focus on one-dimensional (1D) and 2D disordered systems with long-range random hopping amplitudes in both the strong and the weak disorder regime. At the macroscopic limit, it is shown that $f(\alpha)$ is parabolic in the weak disorder regime. In the case of strong disorder, on the other hand, $f(\alpha)$ strongly deviates from parabolicity. Within our numerical uncertainties it has been found that all corrections to the parabolic form vanish at some finite value of the coupling strength.Comment: RevTex4, 6 two-column pages, 4 .eps figures, new results added, updated references, to be published in Phys. Rev.