title: Disorder averaging and finite-size scaling
abstract: 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 predictions are fulfilled only by the new average.
authors.affiliation: Institut Non-Lineaire de Nice, Universite de Nice-Sophia Antipolis, 1361 route des Lucioles, 06560 Valbonne, France.
authors.initials: K
authors.lastname: Bernardet
authors.initials: F
authors.lastname: Pazmandi
authors.initials: GG
authors.lastname: Batrouni