Statistical Mechanics of Incommensurate Phases and Phase Transitions

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This project is a study of one-dimensional systems in which competing interactions with different length scales give rise to a succession of commensurate and incommensurate phases. Their methods open up new possibilities for understanding commensurate-incommensurate phase transitions. In this context they will examine a selection of interesting and accessible problems: non-convex interactions, multicritical points, mean- field theories of selected models, modeling of a qusi-periodic potential, superconducting networks, mathematical correspondence between ground states and more general equilibrium states.