  We face the problem of phase transitions in diluted systems both from
theoretical and numerical sides. We study the effects of quenched site-dilution
in classical models (Heisenberg, Ising and Potts) in 2, 3, and 4 dimensions
both by using the Renormalization Group and numerical simulations in the
canonical and microcanonical ensembles. We propose and check a new formulation
of the Finite Size Scaling ansatz (FSS) inside the microcanonical ensemble. We
use microcanonical simulations to obtain a clear fist-order behavior for the
diluted Potts model in 3D, estimating the tricritical dilution. We perform
large-scale simulations of the 3D diluted Heisenberg model, checking its
self-averaging properties. Finally we study the 4D diluted Ising model
obtaining from the FSS of the specific heat a clear differentiation between the
existing conflicting theories. We also compiled a large number of appendix that
we expect to be used as future reference.
