| Summary: | Over the past few decades, interest has grown in classical and quantum phase transitions that cannot be understood in terms of a Landau–Ginzburg–Wilson (LGW) theory. These unconventional transitions, which are often accompanied by other exotic phenomena, such as topological order and confinement of fractionalized excitations, are known to exist in strongly correlated systems such as the dimer model.
This thesis investigates a novel 'non-LGW' phase transition in the classical double dimer model, consisting of two coupled replicas of the standard dimer model, which has no symmetry-breaking order parameter. It can be understood as a 'pure' topological or confinement transition, and we utilize these properties to distinguish the phases.
In two dimensions, we find a Berezinskii–Kosterlitz–Thouless transition at zero critical coupling, using a symmetry-based analysis of an effective height theory. Meanwhile, on the cubic lattice, we use Monte Carlo simulations to measure the (nonzero) critical coupling and critical exponents, the latter being compatible with the 3D inverted-XY universality class.
Furthermore, we map out the full phase plane when aligning interactions are added for dimers within each replica. In the square-lattice case, we are able to calculate the shape of the phase boundary in the vicinity of the noninteracting point exactly, starting from Lieb's transfer-matrix.
In arriving at this result, we also derive several results of general significance for the square-lattice dimer model. First, we rederive a host of known exact results from Lieb's transfer matrix, many of which were previously derived in the 1960's using Pfaffian methods. Second, we rigorously derive the continuum height description from the microscopic model using the technique of bosonization.
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