We investigate numerically the inverse participation ratio, P2, of the 3D
Anderson model and of the power-law random banded matrix (PRBM) model at
criticality. We found that the variance of lnP2 scales with system size
L as σ2(L)=σ2(∞)−AL−D2/2d, being D2 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.Comment: RevTex, 5 pages, 4 eps figures, to be published in Phys. Rev. Let