Ensemble renormalization group for the random field hierarchical model

The Renormalization Group (RG) methods are still far from being completely understood in quenched disordered systems. In order to gain insight into the nature of the phase transition of these systems, it is common to investigate simple models. In this work we study a real-space RG transformation on the Dyson hierarchical lattice with a random field, which led to a reconstruction of the RG flow and to an evaluation of the critical exponents of the model at T = 0. We show that this method gives very accurate estimations of the critical exponents, by comparing our results with the ones obtained by some of us using an independent method.