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Fluctuations of the correlation dimension at metal-insulator transitions

E. Cuevas·M. Ortuno·V. Gasparian·A. Perez-Garrido
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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 $σ^2(L)=σ^2(\infty)-A L^{-D_2/2d}$, 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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E. Cuevas, M. Ortuno, V. Gasparian, A. Perez-Garrido. 2001-11-07. Fluctuations of the correlation dimension at metal-insulator transitions. https://doi.org/10.1103/physrevlett.88.016401

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