Topological phases and phase transitions in magnets and ice

The main focus of this Thesis is the behaviour of two-dimensional materials,namely (anti)-ferromagnetic materials in the first two chapters, which showtopological phases, and energetic square ice in the third and fourth chapter.The magnetic materials are of interest in part due to foreseen practical applicationsin which skyrmions can act as data carriers for which we have shownthat skyrmions can exist in the ground state. Energetic square ice is of theoreticalinterest due to its anomalous behaviour at the infinite-order phasetransition and as a purely mathematical analytically solvable model. We usedthis model to test the order parameter we constructed that, by definition, canbe used to detect these infinite-order phase transitions. We also show agreementbetween conjectured and known properties for energetic square icewith special boundaries and show the existence of oscillations that go beyondcurrent theories.Theoretical Physic