This project aims to get a theoretical understanding of the most important large-scale phenomena in classical and quantum disordered systems. Thanks to the renormalization group approach the critical behaviour of pure systems is under very good control; however disordered systems are in many ways remarkably peculiar (think for example to non-perturbative phenomena like Griffiths singularities), often the conventional approach does not work and many crucial issues are still unclear. My work aims to fill this important hole in our understanding of disordered systems. I will concentrate my efforts on some of the most important and studied systems, i.e. spin glasses, random field ferromagnets (that are realized in nature as diluted antiferromagnets in a field), Anderson and Mott localization (with possible experimental applications to Bose-Einstein condensates and to electron glasses), surface growth in random media (KPZ and DLA models). In this project I want to pursue a new approach to these problems. I aim to compute in the most accurate way the properties of these systems using the original Wilson formulation of the renormalization group with a phase space cell analysis; this is equivalent to solving a statistical model on a hierarchical lattice (Dyson-Bleher-Sinai model). This is not an easy job. In the same conceptual frame we plan to use simultaneously very different techniques: probabilistic techniques, perturbative techniques at high orders, expansions around mean field on Bethe lattice and numerical techniques to evaluate the critical behaviour. I believe that even this restricted approach is very ambitious, but that the theoretical progresses that have been done in unveiling important features of disordered systems suggest that it will be possible to obtain solid results.
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