Mathematical Studies of Short-Range Spin Glasses In and Out of Equilibrium

短程自旋玻璃平衡态和非平衡态的数学研究

• 批准号: 1207678
• 负责人: Daniel Stein
• 金额: $ 50.5万
• 依托单位: New York University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2012
• 资助国家: 美国
• 起止时间: 2012-09-01 至 2016-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1207678&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 multiplicity, structure and organization of pure phases and ground states; non-equilibrium dynamics; and the presence or absence of a thermodynamic phase transition. The relations between spin glasses and problems in combinatorial optimization, biology, and other areas will also be investigated.This award will support the development of mathematical techniques to be applied to investigations of an important class of magnetic materials known as spin glasses. Understanding their behavior is essential to filling a gap in our knowledge of how materials behave when their structure is dominated by randomness and disorder. The techniques developed will also have potential applications to a wide range of complex problems in other areas, such as computer science and biology. Examples of such problems are route scheduling of airlines and predicting the geometric structure (and hence biological function) of proteins. Some of the research done under this award will be carried out by Ph.D. students as a central part of their graduate training.

这个项目解决了一些关于短程自旋玻璃和其他模型的材料与淬火无序的低温行为的基本问题。严格和启发式的数学方法将应用于分析纯相和基态的多重性，结构和组织;非平衡动力学;以及热力学相变的存在或不存在。此外，还将研究自旋玻璃与组合优化、生物学等领域的问题之间的关系。该奖项将支持数学技术的发展，用于研究一类重要的磁性材料，即自旋玻璃。了解它们的行为对于填补我们对材料在其结构由随机性和无序性主导时如何表现的知识空白至关重要。所开发的技术也将有可能应用于其他领域的广泛复杂问题，如计算机科学和生物学。 这类问题的例子是航空公司的航线调度和预测蛋白质的几何结构（以及生物功能）。在这个奖项下完成的一些研究将由博士进行。学生作为他们的研究生培养的核心部分。