This dissertation studies the effects of quenched disorder on classical, quantum and nonequilibrium phase transitions. After a short introduction which covers the basic concepts of phase transitions, finite-size scaling and random disorder, the dissertation focuses on four separate but related projects. First, we investigate the influence of quenched disorder with long-range spatial correlations on the nonequilibrium phase transitions in the contact process. We show that the long-range correlations increase the probability to find rare atypical regions in the sample. This leads to enhanced Griffiths singularities and changes the universality class of the transition.

Project 2 and 3 focus on disorder at first-order phase transitions. In project 2, we analyze the phase transitions of a classical Ashkin-Teller magnet. We demonstrate that the first-order classical phase transition is destroyed by disorder, and the resulting continuous transition belongs to the clean two-dimensional Ising universality class with logarithmic corrections.

Project 3 investigates the fate of the first-order quantum phase transition in the quantum Ashkin-Teller model by large-scale Monte Carlo simulations. We find that disorder rounds the first-order quantum phase transition just as in the classical case. The resulting critical behavior depends on the strength of the inter-color coupling in the quantum Ashkin- Teller model. This leads to two different regimes, the weak and strong coupling regimes, both of which feature infinite-randomness critical behavior but in different universality classes.

Finally, we study the quantum phase transition of a disordered nanowire from superconductor to metallic behavior. We show that the critical behavior is of infinite-random type and belongs to the random transverse-field Ising universality class as predicted by strong disorder renormalization group results.