Universal and non-universal features of the multifractality exponents of   critical wave-functions
  We calculate perturbatively the multifractality spectrum of wave-functions in critical random matrix ensembles in the regime of weak multifractality. We show that in the leading order the spectrum is universal, while the higher order corrections are model-specific. Explicit results for the anomalous dimensions are derived in the power-law and ultrametric random matrix ensembles. 
I. Rushkin, A. Ossipov, Y. V. Fyodorov
cond-mat.dis-nn