Renormalization group and critical properties of Long Range models

We study a Renormalization Group transformation that can be used also for models with quenched disorder, like spin glasses, for which a commonly accepted and predictive Renormalization Group does not exist. We validate our method by applying it to a particular long-range model, the hierarchical one (both the diluted ferromagnetic version and the spin glass version), finding results in agreement with Monte Carlo simulations. In the second part we deeply analyze the connection between long-range and short-range models that still has some unclear aspects even for the ferromagnet. A systematic analysis is very important to understand if the use of long range models is justified to study properties of short range systems like spin-glasses.