Abstract:
Phase transitions accompanied by spontaneous breaking of continuous symmetries have
been studied extensively in condensed matter and high energy physics. In this thesis we
investigate the spontaneous breaking of discrete symmetries, specifically in spin models
with three-fold, four-fold and higher discrete symmetries. We show that an interplay
between the topological defects - domain walls and vortices - in these models drives
the discrete symmetry to be completely broken, partially broken and even enhanced to a
continuous U(1) symmetry. We show that in two dimensions, percolation of domain walls
drives a transition from a symmetry broken ordered phase to a symmetry enhanced quasi
long range ordered phase which, in turn, undergoes a transition to the symmetry restored
disordered phase when vortices proliferate. We highlight a flaw in the standard method
for calculating winding numbers and propose a new method which correctly identifies
vortices. We show that suppression of vortices in models with even number of states leads
to an intermediate partially ordered phase and that additional suppression of domain walls,
separating opposite spin states, is required to manifest the symmetry enhanced phase. We
show that spin models with three or higher number of states exhibit a partial symmetry
broken phase instead of symmetry enhanced phase in three dimensions as individual types
of domain walls are able to percolate on their own. We also obtain a variety of phases by
suppressing defects belonging to subgroups of the model’s symmetry. Upon enhancing
the formation of vortices instead of suppressing them, we obtain a vortex-antivortex lattice
phase in two dimensions and a vortex condensate phase in three dimensions.
