Lattice-Statistical Models and Applications

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9313648 Wu This renewal grant concerns theoretical studies of lattice models in statistical mechanics with emphases on exact results and applications. Lattice models which retain the essential physics of real systems are crucial in materials research. The research will include the study of several two-and three-dimensional systems which describe a wide range of physical phenomena ranging from adsorption, percolation, directed polymers, and membrane transitions, to high temperature superconductors. In addition, results of lattice model studies will be applied to analyze several long-standing unresolved problems in the mathematical theory of knots. %%% ***