Studies of Exactly Solvable Models in Statistical Mechanics

这是一个持续的研究项目，用于研究手性波茨或广义手性时钟模型中许多尚未解决的问题。引入了一些特殊情况作为研究不相称态、润湿和相对不相称相变的有效模型。当不同层中的分子尺寸不相容时，这种现象就会发生在表层中；生物膜中的波纹态就是一个例子。从数学的角度来看，本研究讨论了一类新的循环超几何函数，与最近发现的精确解有关。将追求新的结果，并进一步探索数学、物理和其他科学各个领域之间的联系。新的结构和模型将进一步研究与分析手段，符号操作和数值技术，如蒙特卡罗分析和系统在有限条与边界上的平均场。这将有助于更好地理解更一般的模型。

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.