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

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。严格和启发式的数学方法将被用来分析纯相和基态的多样性、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。该奖项还将研究自旋玻璃与组合优化、生物学和其他领域中的问题的关系。该奖项将支持数学技术的发展，以应用于一类重要的磁性材料--自旋玻璃的研究。了解它们的行为对于填补我们在材料结构被随机性和无序主导时的行为知识方面的空白至关重要。所开发的技术还将潜在地应用于其他领域的广泛复杂问题，如计算机科学和生物学。这类问题的例子包括航空公司的航线安排和预测蛋白质的几何结构(从而预测生物功能)。在该奖项下完成的一些研究将由博士生进行，作为他们研究生培训的核心部分。

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.