Fluctuations of the correlation dimension at metal-insulator transitions

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.