Non-universal exponents at the Anderson transition

Fluctuations of the correlation dimension D2 describing multifractal properties of critical wavefunctions at the two- and three-dimensional Anderson transition points are studied by employing the forced-oscillator method and the box-counting procedure. We show that the width of the distribution function of D2 over disorder realizations remains finite even in the thermodynamic limit. Similar results are obtained for the exponent α characterizing quantum diffusion at criticality. These imply that exponents defined at the critical point may not be universal. It is also shown that the scaling relation D2=dα (d is the spatial dimension) does not hold for individual samples, but is the case in a statistical sense.