Physics Commons^™

Exact Results In Model Statistical Systems, Peter H. Kleban

University of Maine Office of Research Administration: Grant Reports

Intellectual merit: This project focuses on continued research on the exact study of the statistical mechanics of model systems. The research concentrates on two areas:

1) critical percolation in two dimensions, an important and very extensively studied model system, to which we are bringing new and unexpected approaches, and

2) the thermodynamics of the Farey fraction spin chain, a set of one dimensional models with interesting phase transition behavior and connections to multifractals, and dynamical systems.

This project aims at new results and insights in both these areas. Research on the Farey models illuminates an interesting borderline case in the …