Studies of Exactly Solvable Models in Statistical Mechanics

统计力学中精确可解模型的研究

• 批准号: 0100041
• 负责人: Jacques H Perk
• 金额: $ 16.5万
• 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: 2001
• 资助国家: 美国
• 起止时间: 2001-08-01 至 2005-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0100041&HistoricalAwards=false
• 关键词: Studies; Exactly; Solvable; Models; Statistical

0100041Perk and Au-YangThis is a research project for the study of exactly solvable models of statistical mechanics, including the integrable chiral Potts model and various Ising models. These models will be studied by exact analytical and approximate numerical methods. Various physical phenomena will be studied, such as critical phenomena in quasi-periodic or aperiodic lattices, commensurate-incommensurate phase transitions, and frustration. The impact of frustration on the wavevector-dependent susceptibility will be analyzed by studying partially and fully frustrated triangular or checkerboard Ising models. New algorithms for the susceptibility series of planar Ising models, whose complexity grow polynomially, will be developed and the resulting long series expansions will be analyzed to get a better understanding of corrections to scaling. Many challenging problems remaining to be solved within the integrable chiral Potts model, such as the magnetization, spin-spin and energy-energy correlations. By its very nature, this project also involves several areas of mathematics of current interest.

0100041 Perk和Au-Yang这是一个研究统计力学精确可解模型的研究项目，包括可积手征Potts模型和各种Ising模型。 这些模型将通过精确分析和近似数值方法进行研究。 各种物理现象将被研究，如准周期或非周期晶格中的临界现象，相变-无公度相变和挫折。 通过研究部分和完全受挫三角形或棋盘伊辛模型，将分析挫折对波矢相关磁化率的影响。 平面伊辛模型，其复杂性的多项式增长的磁化率系列的新算法，将开发和由此产生的长系列扩展将进行分析，以更好地了解校正缩放。 在可积手征Potts模型中还有许多具有挑战性的问题有待解决，如磁化强度、自旋-自旋和能量-能量关联等。 就其本质而言，该项目还涉及当前感兴趣的几个数学领域。