The phase diagram of the diluted antiferromagnet in a field at zero temperature

The discussion of disordered systems such as the diluted antiferromagnet in a field (DAFF) is highly controversial. Classical approaches like the renormalization group lead to contradictory results. This thesis presents alternative methods for the understanding of the low temperature regime of the DAFF. The results help to identify misunderstandings and misleading assumptions in the recent research literature.; The phase diagram of the DAFF ground state is established by a Bethe lattice mean-field theory and exact simulations of the ground state in three dimensions. By introducing an appropriate order parameter for the ground state, it is found that the DAFF exhibits three different phases. This stands in contrast to the ground state of the 3d Random Field Ising Model (RFIM) which exhibits two different phases, although the RFIM and the DAFF are supposed to be in the same universality class.; The mean-field theory phase diagram is derived by a new technique for the Bethe lattice which can also be applied to other systems. The ground state simulations are used to establish the phase diagrams for the cubic and the BCC lattice.