Mathematical Sciences: Solvable Lattice Models in Statistical Mechanics

数学科学：统计力学中的可解晶格模型

• 批准号: 8700867
• 负责人: Craig Tracy
• 金额: $ 7.81万
• 依托单位: University of California-Davis
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1987
• 资助国家: 美国
• 起止时间: 1987-07-01 至 1990-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8700867&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Solvable; Lattice; Models

This research program will explore the connections between exactly solvable lattice models in lattice statistical mechanics and the representation theory of Kac-Moody Lie algebras. The long term goal is to connect the present understanding of exactly solvable models with that of the representation theory of certain Kac-Moody Lie algebra. The immediate task will be the study of specific solvable models and their relations to loop groups. Successful accomplishment of the immediate research project will enhance the methodology for solvable models in the statistical mechanics aspects of physics. This in turn will lead to a better understanding, utilization and control of materials and matters in technical applications as well as in our daily life.

该研究项目将探索晶格统计力学中精确可解的晶格模型与 Kac-Moody 李代数表示理论之间的联系。 长期目标是将目前对精确可解模型的理解与某些 Kac-Moody 李代数的表示论的理解联系起来。 当前的任务是研究特定的可解模型及其与循环群的关系。 近期研究项目的成功完成将增强物理学统计力学方面可解模型的方法。 这反过来将导致我们更好地理解、利用和控制技术应用和日常生活中的材料和物质。