Studies of Exactly Solvable Models in Statistical Mechanics

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This is a continuing research project for the study of many of the unsolved problems in chiral Potts or generalized chiral clock models. Special cases have been introduced as effective models for the study of incommensurate states, wetting, and commensurate-incommensurate phase transitions. Such phenomena can occur in surface layers when the molecules in different layers have incompatible sizes; an example is ripple states in biomembranes. From a mathematical point of view, this research addresses a new class of cyclic hypergeometric functions, related to exact solutions found recently. New results will be pursued and connections between various fields of mathematics, physics, and other sciences will be further explored. New structures and models will be investigated further with analytic means, symbolic manipulation and numerical techniques, such as Monte Carlo analysis and systems on finite strips with mean fields on the boundaries. This should lead to better understanding of more general models.