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

小行星9307816 这是一个研究项目的手征Potts模型，广义手征Potts模型，和多组分手征Potts模型中的许多未解决的问题的研究的延续。 这些数学模型描述了相变在实验上可实现的系统，如吸附的分子在薄膜，多层系统，膜等，尽管许多成功迄今在计算各种物理量的手性Potts模型，这些结果尚未得到充分的探讨和利用。 该项目旨在将精确的结果翻译成物理学家更透明的语言，以便Monte Carlo计算，高温和低温膨胀以及各种其他方法的专家可以使用它们。 然后，精确的结果可以用来正确衡量近似方法的误差，并解决长期存在的争议。 将与我们的俄罗斯同事Yu. G.合作，尝试获得新的三维可解模型。斯特罗加诺夫 这项工作的进展可能会带来数学和物理学中许多其他研究领域之间的相互作用，如量子群和纽结理论，单极子和弦理论，凝聚态物质的相变，以及生物物理学中的生物膜。 ! ! 一 ( Times New Roman 符号Arial " H ; % ; % / 特里湖希克斯特里湖希克斯