Mathematical Sciences: Statistical Mechanics of Disordered Systems and Conformal Field Theory

数学科学：无序系统的统计力学和共形场论

• 批准号: 8903041
• 负责人: Antii Kupiainen
• 金额: $ 10.7万
• 依托单位: Rutgers University New Brunswick
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1989
• 资助国家: 美国
• 起止时间: 1989-06-01 至 1992-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8903041&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Statistical; Mechanics; Disordered

Professor Kupiainen's research project in statistical mechanics has two parts, one in the physics of disordered systems and the other in the application of conformal field theory to two-dimensional critical phenomena. In connection with disordered systems, he will endeavor to develop exact renormalization group methods for the study of random walks in random environments, of interface fluctuations in the presence of random fields or random exchange couplings, and of spin glass models. On the conformal field theory side, he will continue investigations in which the Wess-Zumino-Witten model is used to solve various conformal theories. Statistical mechanics studies the behavior of systems consisting of very large numbers of particles interacting with one another. Typically, the particles would be arrayed in a lattice and interactions would take place between nearest neighbors. The basic problem is predict the overall, long-run behavior (equilibria, phase transitions, and the like) of the system given information about the interactions. Mathematically, this is a very difficult undertaking even in the simplest models. A further complication occurs when elements of randomness are present, as in the research to be undertaken by Professor Kupiainen.

Kupiainen教授的统计研究项目 力学有两个部分，一个是无序系统的物理学 另一个是共形场论在 二维临界现象关于无序 系统，他将奋进发展精确的重整化群 随机环境中随机游动的研究方法 存在随机场或随机场时的界面波动 交换耦合和自旋玻璃模型。关于共形 场理论方面，他将继续调查，其中 Wess-Zumino-维滕模型用于求解各种共形 理论 统计力学研究系统的行为 由大量的粒子相互作用组成 彼此典型地，颗粒将排列成 晶格和相互作用将发生在最近的 邻居基本问题是预测整体的、长期的 的行为（平衡、相变等）。 系统给出了关于交互的信息。从数学上讲， 即使在最简单的模型中，这也是一项非常困难的任务。 当随机性的元素 目前，如在教授进行的研究 库皮艾宁