Mathematical Sciences: Exact Analysis of Lattice Statistics Models and Applications

数学科学：格统计模型和应用的精确分析

• 批准号: 9106521
• 负责人: Jacques H Perk
• 金额: $ 9.8万
• 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: 1991
• 资助国家: 美国
• 起止时间: 1991-07-01 至 1994-03-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9106521&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Exact; Analysis; Lattice

In this project the principal investigators will continue their study of new, higher-genus solutions of the Yang-Baxter equation in the chiral Potts model. These solutions describe phase transitions in experimentally realizable systems and they serve as representatives of various universality classes. In addition, the principal investigators will look at spin-spin correlation functions of the Z-invariant inhomogeneous Ising model on an irregular lattice, in order to obtain the correlation functions of certain quasicrystals and some quasiperiodic Ising lattices. Models in statistical mechanics are an important vehicle for improving our understanding of ordered structures such as crystals. In addition, the study of models like the chiral Potts model involves a nice interplay between mathematics and physics that serves to enhance both fields. In this project the principal investigators will look for new solutions of the Yang- Baxter equation that describe quasicrystals and quasiperiodic lattices. This work touches upon other topics on the border between mathematics and physics such as quantum groups and knot theory, monopoles and string theory, phase transitions in condensed matter and biomembranes in biophysics.

在这个项目中，主要研究人员将继续研究手性波茨模型中杨-巴克斯特方程的新的高格解。这些解描述了实验可实现系统中的相变，它们是各种通用性类的代表。此外，主要研究者将研究不规则晶格上z不变非齐次Ising模型的自旋-自旋相关函数，以获得某些准晶体和某些准周期Ising晶格的相关函数。统计力学中的模型是提高我们对有序结构（如晶体）理解的重要工具。此外，对像手性波茨模型这样的模型的研究涉及数学和物理之间的良好相互作用，有助于增强这两个领域。在这个项目中，主要研究人员将寻找描述准晶体和准周期晶格的Yang- Baxter方程的新解。这项工作涉及数学和物理之间边界的其他主题，如量子群和结理论，单极子和弦理论，凝聚态物质的相变和生物物理学中的生物膜。