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The disorder induced metal--insulator transition is investigated in athree-dimensional simple cubic lattice and compared for the presence andabsence of time-reversal and spin-rotational symmetry, i.e. in the threeconventional symmetry classes. Large scale numerical simulations have beenperformed on systems with linear sizes up to $L=100$ in order to obtaineigenstates at the band center, $E=0$. The multifractal dimensions, exponents$D_q$ and $\alpha_q$, have been determined in the range of $-1\leq q\leq 2$.The finite-size scaling of the generalized multifractal exponents provide thecritical exponents for the different symmetry classes in accordance with valuesknown from the literature based on high precision transfer matrix techniques.The multifractal exponents of the different symmetry classes provide furthercharacterization of the Anderson transition, which was missing from theliterature so far.

Finite-size scaling and multifractality at the Anderson transition for the three Wigner-Dyson symmetry classes in three dimensions