  We propose a new picture of the renormalization group (RG) approach in the
presence of disorder, which considers the RG trajectories of each random sample
(realization) separately instead of the usual renormalization of the averaged
free energy. The main consequence of the theory is that the average over
randomness has to be taken after finding the critical point of each
realization. To demonstrate these concepts, we study the finite-size scaling
properties of the two-dimensional random-bond Ising model. We find that most of
the previously observed finite-size corrections are due to the sample-to-sample
fluctuation of the critical temperature and scaling is more adequate in terms
of the new scaling variables.
