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The phase diagram of the metal-insulator transition in a three dimensional quantum percolation problem is investigated numerically based on the multifractal analysis of the eigenstates. The large scale numerical simulation has been performed on systems with linear sizes up to $L=140$. The multifractal dimensions, exponents $D_q$ and $alpha_q$, have been determined in the range of $0leq qleq 1$. Our results confirm that this problem belongs to the same universality class as the three dimensional Anderson model, the critical exponent of the localization length was found to be $ u=1.622pm 0.035$. The mulifractal function, $f(alpha)$, appears to be universal, however, the exponents $D_q$ and $alpha_q$ produced anomalous variations along the phase boundary, $p_c^Q(E)$.
We describe a new multifractal finite size scaling (MFSS) procedure and its application to the Anderson localization-delocalization transition. MFSS permits the simultaneous estimation of the critical parameters and the multifractal exponents. Simula
We have investigated the phase transition in the Heisenberg spin glass using massive numerical simulations to study larger sizes, 48x48x48, than have been attempted before at a spin glass phase transition. A finite-size scaling analysis indicates tha
We use multifractal finite-size scaling to perform a high-precision numerical study of the critical properties of the Anderson localization-delocalization transition in the unitary symmetry class, considering the Anderson model including a random mag
Generalized multifractality characterizes scaling of eigenstate observables at Anderson-localization critical points. We explore generalized multifractality in 2D systems, with the main focus on the spin quantum Hall (SQH) transition in superconducto
Many-body localization (MBL) is well characterized in Fock space. To quantify the degree of this Fock space localization, the multifractal dimension $D_q$ is employed; it has been claimed that $D_q$ shows a jump from the delocalized value $D_q=1$ in