Graduation Year


Document Type




Degree Granting Department


Major Professor

David A. Rabson

Co-Major Professor

Chun-Min Lo


cancer, fractional Brownian motion, magnetic anisotropy, magnetic multilayers, random walk


This work is a study of complex many-body systems with non-trivial interactions. Many such systems can be described with models that are much simpler than the real thing but which can still give good insight into the behavior of realistic systems. We take a look at two such systems. The first part looks at a model that elucidates the variety of magnetic phases observed in rare-earth heterostructures at low temperatures: the six-state clock model. We use an ANNNI-like model Hamiltonian that has a three-dimensional parameter space and yields two-dimensional multiphase regions in this space. A low-temperature expansion of the free energy reveals an example of Villain's `order from disorder' [81, 60] when an infinitesimal temperature breaks the ground-state degeneracy. The next part of our work describes biological systems. Using ECIS (Electric Cell-Substrate Impedance Sensing), we are able to extract complex impedance time series from a confluent layer of live cells. We use simple statistics to characterize the behavior of cells in these experiments. We compare experiment with models of fractional Brownian motion and random walks with persistence. We next detect differences in the behavior of single cell types in a toxic environment. Finally, we develop a very simple model of micromotion that helps explain the types of interactions responsible for the long-term and short-term correlations seen in the power spectra and autocorrelation curves extracted from the times series produced from the experiments.