Lattice-Statistical Models and Applications

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9614170 Wu This project is concerned with theoretical studies of lattice models in statistical physics with emphasis on exact results and applications. While most exact results are limited to 2-dimensions, this project proposes to study the 3-dimensional systems by building around the 2-d solution. Specific plans include: analysis of the relationship between a quantum spin system in 2-dimension and a classical one in 3-d, further work on certain conjectures on the distribution of zeroes of the Potts model partition function and directed percolation problem in 3-d. Additional projects involve: investigation of roughening of crystal surfaces, gel-sol transition in a ternary polymer solution, the mathematical problem of restricted partitions of an integer and derivation of a new link invariant in the theory of knots and kinks. %%% This PI is widely known for his contributions to more mathematical aspects of the materials related problems. In research on the fundamental properties of materials and phase transitions, this PI has made contributions where the problem has been simplified to the extent that a mathematically exact and rigorous solution is possible. The more realistic problems then can be understood by building up on the exact results. Much of the present grant supports search for exact solutions in bulk (3-dimensional) on certain simplified models where the solution is known for a thin film (in 2-d). ***