In this thesis I present studies of the non-equilibrium dynamics of Ising and Potts ferromagnets in two spatial dimensions. While the conception of these models was originally motivated by a desire to understand the phenomena surrounding equilibrium phase transitions, they have found considerable use in non-equilibrium Statistical Physics. Despite being well studied, even from a non-equilibrium viewpoint, a number of surprisingly basic and fundamental gaps in our understanding of Ising and Potts models have come to light in recent decades. For example, the tacit assumption that Ising ferromagnets should always reach their ground state at zero-temperature has been found incorrect, and unexpected features of the associated relaxation process have come to light. With the Potts model the situation is stranger still: the late time final states that persist in two dimensions are considerably richer than those of the Ising model, and the relaxation times are complex and not yet well understood. In this thesis I examine basic aspects of zero-temperature coarsening in two dimensional Ising and Potts ferromagnets. I explore the timescales associated with zero-temperature freezing in the Ising model, and uncover the existence of an overlooked relaxation timescale. I then investigate the final states of the zero-temperature Potts model on the triangular lattice, which prior to this work had not been examined. I continue my studies of the Potts model to situations of increased ground state degeneracy and extended local interaction rules.
|Date of Award||28 Jul 2020|
- University Of Strathclyde
|Sponsors||EPSRC (Engineering and Physical Sciences Research Council)|
|Supervisor||Ben Hourahine (Supervisor) & Oliver Henrich (Supervisor)|