Fractal dimensions of eigenfunctions for various critical random matrix
ensembles are investigated in perturbation series in the regimes of strong and
weak multifractality. In both regimes we obtain expressions similar to those of
the critical banded random matrix ensemble extensively discussed in the
literature. For certain ensembles, the leading-order term for weak
multifractality can be calculated within standard perturbation theory. For
other models such a direct approach requires modifications which are briefly
discussed. Our analytical formulas are in good agreement with numerical
calculations.Comment: 28 pages, 7 figure