The Kosterlitz-Thouless transition in helium-4 films and spiral spin systems
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1995
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This research studies phase transitions in two-dimensional systems with a continuous symmetry group. In 1966 Mermin and Wagner showed that such systems exhibit no true long range order(l). However, they still undergo a phase transition at a critical temperature T, from a high temperature phase, where the order parameter correlation function decays exponentially, to a low temperature phase, where the correlation function has a power law decay (2). This transition is mediated by thermally excited topological point defects (vortices) in the order parameter and is commonly referred to as a Kosterlitz-Thouless(KT) transition. The two systems studied in this work, which both have a KT transition, are thin superfluid films, where the gradient of the order parameter is identified with the superfluid velocity, and classical XY spins on a two-dimensional square lattice, where the order parameter is the orientation of the spins. algorithm allows the system to choose its own boundary conditions. This enables one to accurately determine the period of the spiral as a function of temperature. By monitoring the fluctuations in the period the spin wave stiffness is calculated. The algorithm is applied to 2 and 3 dimensional lattices of classical XY spins. In the 2 dimensional case the nature of the transition from the ordered to the disordered phase is investigated by comparing the Monte Carlo stiffness to predictions based on a theory that assumes a Kosterlitz-Thouless transition.The first part of this dissertation investigates the effect of substrate inhomo-geneities on the Kosterlitz-Thouless transition in thin superfluid4He films. In recent torsional oscillator experiments (3) with thin He films the data was analyzed assuming that the dissipation at the KT transition was only due to vortex dynamics. This assumption led to a smaller dissipation than was observed experimentally. We re-analyze existing torsional oscillator data by including the additional dissipation due to inhomogeneities in the substrate. From the new analysis we estimate how inhomogeneous the substrate must be to explain the data. The second part of this.dissertation studies incommensurate spiral magnetic systems by computer simulation based on a new Monte Carlo algorithm(4). The new algorithm allows the system to choose its own boundary conditions. This enables one to accurately determine the period of the spiral as a function of temperature. By monitoring the fluctuations in the period the spin wave stiffness is calculated. The algorithm is applied to 2 and 3 dimensional lattices of classical XY spins. In the 2 dimensional case the nature of the transition from the ordered to the disordered phase is investigated by comparing the Monte Carlo stiffness to predictions based on a theory that assumes a Kosterlitz-Thouless transition.
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Major physics