In this book unbiased numerical techniques are applied to the study of two of the most important current problems in condensed matter physics: magnetically doped III-V semiconductors and high-temperature superconductors. The first part of the book mainly focus on the first full-scale study of a realistic model for the III-V Mn-doped semiconductors using state-of-the-art numerical techniques. More specifically, a real-space Hamiltonian with the fcc lattice structure that reproduces the valence bands of undoped GaAs are constructed. In addition, two-band model and a new phenomenological...