Mathematical Studies of Short-Range Spin Glasses

短程自旋玻璃的数学研究

• 批准号: 1106316
• 负责人: Daniel Stein
• 金额: $ 11.3万
• 依托单位: New York University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2011
• 资助国家: 美国
• 起止时间: 2011-08-15 至 2013-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1106316&HistoricalAwards=false
• 关键词: Mathematical; Studies; Short; Range; Spin

This project addresses a number of basic questions concerning the low temperature behavior of short-range spin glasses and other models of materials with quenched disorder. Rigorous and heuristic mathematical methods will be applied to analyze the conjectured presence of a phase transition; the multiplicity, structure and organization of pure phases and ground states; the effect of small magnetic fields; and non-equilibrium dynamics.The purpose of this project is to develop mathematical techniques and results in certain specific models of low temperature materials, known as spin glasses. The importance of the project is that these techniques have potential application to a wide range of problemsarising in areas such as theoretical computer science or biology which combine issues of complexity and optimization. Examples of such problems are optimal route scheduling of airlines and predicting the geometric structure (and hence biological function) of proteins.

这个项目解决了一些关于短程自旋玻璃和其他具有猝灭无序的材料模型的低温行为的基本问题。严格的和启发式的数学方法将被用来分析推测的相变的存在；纯相和基态的多重性、结构和组织；小磁场的影响；以及非平衡动力学。这个项目的目的是发展数学技术和结果，在某些特定的低温材料模型，称为自旋玻璃。该项目的重要性在于，这些技术有可能应用于理论计算机科学或生物学等领域出现的广泛问题，这些领域结合了复杂性和最优化问题。这类问题的例子包括航空公司的最优航线安排和预测蛋白质的几何结构(从而预测生物功能)。