  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.
