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Some Problems In Statistical Mechanics With Applications To Materials Science, Ethan Ballard

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In this work, some problems in statistical mechanics related to condensed matter physics and of general interst in materials science, physics, chemistry and polymer science are considered. In chapters 1-4, the work by E.M. Lifshitz on the group-theoretical refinements of the Landau theory of phase transitions is brought to completion. Based on mathematical results obtained by Yamabe, Osgood, Phillips, Sarnak, and Kholodenko analytical results for determinants were developed which allows for prediction of the symmetry of the phase after a phase transition provided that the symmetry prior to the phase transition is known. Numerical results are presented which are in …