Fluctuations of the Correlation Dimension at Metal-Insulator Transitions
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 $\mathrm{ln}{P}_{2}$ scales with system size $L$ as ${\ensuremath{\sigma}}^{2}(L)\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}{\ensuremath{\sigma}}^{2}(\ensuremath{\infty}){\ensuremath{-}AL}^{{\ensuremath{-}D}_{2}/2d}$, with ${D}_{2}$ being the correlation dimension and $d$ the system dimension. Therefore …