E. Cuevas

f ( α ) multifractal spectrum at strong and weak disorder

The system size dependence of the multifractal spectrum

Fluctuations of the correlation dimension at metal-insulator transitions

f(\ensuremath{\alpha})

Dimensional dependence of the metal-insulator transition

and its singularity strength

Anomalously large critical regions in power-law random matrix ensembles

\ensuremath{\alpha}

CRITICAL SPECTRAL STATISTICS IN TWO-DIMENSIONAL INTERACTING DISORDERED SYSTEMS

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

Dynamical scaling for critical states: Validity of Chalker's ansatz for strong fractality

f(\ensuremath{\alpha})

Supersymmetric virial expansion for time-reversal invariant disordered systems

is parabolic in the weak disorder regime. In the case of strong disorder, on the other hand,

Differentiable potentials and metallic states in disordered one-dimensional systems

f(\ensuremath{\alpha})

Localized to extended states transition for two interacting particles in a two-dimensional random potential

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.

Many-particle jumps algorithm and Thomson's problem

We investigate numerically the inverse participation ratio, P(2), of the 3D Anderson model and of the power-law random banded matrix (PRBM) model at criticality. We found that the variance of lnP(2) scales with system size L as sigma(2)(L) = sigma(2)(infinity)-AL(-D(2)/2d), with D(2) being the correlation dimension and d the system dimension. Therefore the concept of a correlation dimension is well defined in the two models considered. The 3D Anderson transition and the PRBM transition for b = 0.3 (see the text for the definition of b) are fairly similar with respect to all critical magnitudes studied.