Fluctuations of the correlation dimension at metal-insulator transitions

Abstract

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 $\ln P_2$ scales with system size $L$ as ${\sigma }^2(L)={\sigma }^2(\infty )-A{L}^{-D_2/2d}$, being $D_2$ 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.

RevTex, 5 pages, 4 eps figures, to be published in Phys. Rev. Lett

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