Studies of Exactly Solvable Models in Statistical Mechanics

统计力学中精确可解模型的研究

• 批准号: 9722159
• 负责人: Jacques H Perk
• 金额: $ 15万
• 依托单位: Oklahoma State University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1997
• 资助国家: 美国
• 起止时间: 1997-08-01 至 2001-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9722159&HistoricalAwards=false
• 关键词: Studies; Exactly; Solvable; Models; Statistical

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.

这是一个持续的研究项目，研究手征Potts或广义手征时钟模型中许多未解决的问题。 特殊的情况下，已被引入作为有效的模型研究的无公度状态，润湿，和无公度相变。 当不同层中的分子具有不相容的尺寸时，这种现象可以发生在表面层中;一个例子是生物膜中的涟漪状态。 从数学的角度，本研究解决了一类新的循环超几何函数，最近发现的精确解。 将追求新的成果，并进一步探索数学，物理学和其他科学的各个领域之间的联系。新的结构和模型将进一步研究分析手段，符号操作和数值技术，如蒙特卡洛分析和系统的有限条上的边界上的平均场。这将有助于更好地理解更一般的模型。