Properties of low-dimensional systems
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[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT REQUEST OF AUTHOR.] In this work we study the equilibrium properties of systems in two-dimensions, and the effects that discrete symmetry, space dimensionality, character of the interaction and number of internal degrees of freedom have on the properties of two systems of classical and quantum nature. We investigate macroscopic properties from a family of classical Hamiltonian models with discrete degrees of freedom, and we observed how the discreteness of spin variables can be "washed out" in ensemble averages, where different microscopic interactions between molecules or spins, exhibit identical thermodynamic behavior over a wide range of temperatures. This many-to-one map of intermolecular interactions onto thermodynamic states, demonstrates previously unknown limits for macroscopic distinguishability of different microscopic interactions. Another part of the work is committed to the study of collective modes that would give rise to macroscopic states with discrete symmetries in electron systems in the Fractional Quantum Hall regime. In this approach, we construct broken rotational symmetry states and compute the spectrum of excitations. This study is relevant to the understanding of the Wigner crystallization in the Fractional Quantum Hall Effect, and properties and nature of Quantum Hall Liquid Crystals.
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