Fluctuations of the correlation dimension at metal-insulator transitions

Details Fluctuations of the correlation dimension at metal-insulator transitions Fluctuations of the correlation dimension at metal-insulator transitions

2001-06-28

arxiv.org/abs/cond-mat/0106605v2

Phys. Rev. Lett. 88, 016401 (2002)

Physics

Condensed Matter

Disordered Systems and Neural Networks

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

Scientific paper

10.1103/PhysRevLett.88.016401

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.

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