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.

该研究计划将探讨晶格统计力学中准确可解决的晶格模型与Kac-Moody Lie代数的代表理论之间的联系。 长期目标是将对准确可解决的模型的当前理解与某些kac-moody lie代数的表示理论联系起来。 即时任务将是对特定可解决的模型的研究及其与循环组的关系。 即时研究项目的成功完成将增强物理学统计力学方面的可解决模型的方法。 反过来，这将导致对技术应用以及我们日常生活中材料和事务的更好理解，利用和控制。