This thesis presents four research papers in the field of condensed-matter theory. In all four papers, large-scale Monte Carlo simulations are used to investigate phases and phase transitions in two-component models of superconductors and superfluids with multiple broken symmetries. In Article I, a U(1) × U(1) lattice London superconductor with two different types of intercomponent interactions is investigated with focus on understanding the phases and the phase transitions of the model. Particularly, this model exhibits two different paired phases where proliferation of composite topological defects plays an important role.
In Article II and III, a two-dimensional unconventional two-component Coulomb plasma with two distinct Coulomb interactions is investigated. The plasma relates to inner products of Ising-type quantum Hall states as well as to rotating two-component Bose- Einstein condensates with an intercomponent Andreev-Bashkin drag interaction. We investigate the phases and phase transitions of this plasma. Depending on the strength of the attractive intercomponent interaction, the plasma can undergo a Berezinskii- Kosterlitz-Thouless charge-unbinding transition. It can also undergo a two-dimensional melting transition when there is a strong intracomponent repulsion for one of the components. For the parameter values corresponding to the Ising-type quantum Hall states, the plasma is in a screening phase. This can be used to demonstrate that Ising-type quantum Hall states possess quasiparticles with exotic properties.
In Article IV, the noncompact CP1 model is investigated. This model is proposed as a critical field theory of the continuous quantum phase transition between the N´eel state and the paramagnetic valence bond solid state in a quantum antiferromagnet. The model exhibits a direct transition line between a fully ordered phase with broken SU(2) symmetry and a fully disordered phase. By going to larger systems, we find that the bicritical point, which terminates the direct transition line, has been overestimated in earlier works. This may have important consequences for the determination of the character of the phase transition along the direct transition line.