Contribuições Analíticas e Computacionais para Modelos Magnéticos Desordenados

Several disordered magnetic models are investigated in this thesis, through different approximation techniques. Within a mean-field approach, two random-field Ising models that exhibit a rather nontrivial multicritical behavior are analyzed. A rich variety of phase diagrams is presented, with a single or two distinct ferromagnetic phases, continuous and first-order transition lines, tricritical, fourth-order, critical end points, and many other interesting multicritical phenomena. It is argued that one of these models is relevant for the study of some diluted antiferromagnets in the presence of a uniform external field, like the compound ${\rm Fe_{x}Mg_{1-x}Cl_{2}}$, whereas the second one should be pertinent for some plastic-crystal systems. In addition to that, a nearest-neighbor-interaction Ising spin glass, in the presence of an external magnetic field, is studied on different hierarchical lattices. In this case, a spin-glass attractor is found, in the plane magnetic field versus temperature, associated with a low-temperature phase, for hierarchical lattices of fractal dimension around three, as well as for higher dimensions. The physical consequences of this attractor are discussed, in view of the present scenario of the spin-glass problem. Finally, an Ising model with competing ferromagnetic nearest-neighbor interactions and random (ferromagnetic and antiferromagnetic) second-neighbor interactions is considered on a square lattice. Such a model is studied through both an effective-field theory, as well as Monte Carlo simulations. An interesting phase diagram is found, exhibiting both ferromagnetic and superantiferromagnetic phases, as well as a nontrivial critical-exponent behavior.