We analyze the replica-symmetry-breaking (RSB) construction in the Sherrington - Kirkpatrick (SK) model and in the p-state Potts glass for p ≤ 4. We present a general scheme for deriving an asymptotic solution with an arbitrary number of discrete hierarchies of broken replica symmetry near the critical temperature for both models, and close to the de Almeida- Thouless instability line in the SK model. We show that in the SK model all solutions with finite many hierarchies are unstable and only the scheme with infinite many hierarchies becomes marginally stable in the spin-glass phase. For the Potts glass, we find, moreover, an one-step RSB solution which co- exists with the infinite RSB solution for p > p∗ ≈ 2.82. The former solution is locally stable but has lower free energy than the latter which is marginally stable and has the highest free energy. 1

The results reported in this thesis contribute to the understanding of disordered systems, to mesoscopic physics on the one hand, and to the physics of spin glasses on the other hand. The first part of this thesis studies numerically coherent electronic transport in a non magnetic metal accurately doped with frozen magnetic impurities (a low temperature spin glass). Thanks to a recursive code that calculates the two terminal conductance of the system, we study in detail the metallic regime of conduction (large conductance) as well as the insulating regime (small conductance). In both regimes, we highlight a universal behavior of the system. Moreover, a study of correlations between the conductance of different spin configurations of impurities allows us to link these correlations with correlations between spin configurations. This study opens the route for the first experimental determination of the overlap via transport measurements. A second part of this thesis deals with the study of the mean field Sherrington-Kirkpatrick model, which describes the low temperature phase of an Ising spin glass. We are interested here in the generalization of this model to quantum spins (i.e including the possibility to flip by quantum tunneling) of this classical model that was well studied during the past thirty years. We deduce analytically motion equations at the semi-classical level, for which the influence of quantum tunneling is weak, and we compare them with the classical case. We finally solve numerically these equations using a pseudo-spectral method.