Studies of Exactly Solvable Models in Statistical Mechanics

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0100041Perk and Au-YangThis is a research project for the study of exactly solvable models of statistical mechanics, including the integrable chiral Potts model and various Ising models. These models will be studied by exact analytical and approximate numerical methods. Various physical phenomena will be studied, such as critical phenomena in quasi-periodic or aperiodic lattices, commensurate-incommensurate phase transitions, and frustration. The impact of frustration on the wavevector-dependent susceptibility will be analyzed by studying partially and fully frustrated triangular or checkerboard Ising models. New algorithms for the susceptibility series of planar Ising models, whose complexity grow polynomially, will be developed and the resulting long series expansions will be analyzed to get a better understanding of corrections to scaling. Many challenging problems remaining to be solved within the integrable chiral Potts model, such as the magnetization, spin-spin and energy-energy correlations. By its very nature, this project also involves several areas of mathematics of current interest.