Mathematical Sciences: Studies of Exactly Solvable Models in Statistical Mechanics

数学科学：统计力学中精确可解模型的研究

• 批准号: 9307816
• 负责人: Jacques H Perk
• 金额: $ 10.4万
• 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: 1993
• 资助国家: 美国
• 起止时间: 1993-07-15 至 1996-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9307816&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Studies; Exactly; Solvable

9307816 Perk This is a research project for the continuation of the study of many of the unsolved problems in the chiral Potts model, generalized chiral Potts models, and multi-component chiral Potts models. These mathematical models describe phase transitions in experimentally realizable systems such as adsorption of molecules on thin films, multi-layered systems, membranes, etc. In spite of many successes so far in calculating various physical quantities of the chiral Potts model, these results have not yet been fully explored and made use of. It is intended in this project to translate the exact results into language more transparent to physicists, so that experts in Monte Carlo calculations, high- and low-temperature expansions, and various other methods, can use them. The exact results can be then used to properly gauge the errors of the approximate methods and solve long-standing controversies. Attempts to obtain new solvable models in three dimensions will be made in collaboration with our Russian colleague Yu.G. Stroganov. Progress in this work may bring forth interaction between many other research areas in mathematics and physics such as quantum groups and knot theory, monopoles and string theory, phase transitions in condensed matter, and biomembranes in biophysics. ! ! A ( Times New Roman Symbol & Arial " h ; % ; % / terri l. hicks terri l. hicks

9307816 PERK这是一个研究项目，用于继续研究手性Potts模型中许多未解决问题的研究，广泛的手性Potts模型和多组分的手性Potts模型。 这些数学模型描述了在实验可实现的系统中的相变，例如在薄膜上的分子吸附，多层系统，膜等。尽管到目前为止，在计算各种物理量的Chiral Potts模型方面取得了许多成功，但这些结果尚未得到充分探索和使用。 该项目的目的是将确切的结果转化为物理学家更透明的语言，以便蒙特卡洛计算，高温和低温扩展的专家可以使用它们。 然后可以使用确切的结果正确评估近似方法的误差并解决长期存在的争议。 尝试在三个维度上获得新的可解决模型的尝试将与我们的俄罗斯同事Yu.G.斯特罗加诺夫。 这项工作的进展可能会导致数学和物理学的许多其他研究领域之间的相互作用，例如量子组和结理论，单脚和弦理论，凝结物质中的相变，以及生物物理学中的生物膜。 呢 呢 A（时代新罗马符号和arial“ h;％;％ / terril。Hicksterril。Hicks