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This research focuses on the exact study of the statistical mechanics of model systems. Research concentrates on critical percolation in two-dimensions, and important and extensively studied statistical system, and the phase transition of the farey fraction spin chain, a new and interesting one-dimensional model with connections to multifractals and Monte Carol simulations, mathematically exact solutions of model statistical mechanical systems, and techniques from number theory. The goal is to gain new insights into, and understanding of, these systems. An important feature of the project is the use of techniques from pure mathematics and close collaboration with mathematicians.
Kleban, Peter H., "Exact Results in Model Statistical Systems" (2007). University of Maine Office of Research and Sponsored Programs: Grant Reports. 140.