Mathematical Studies of Short-Range Spin Glasses

本项目解决了一些关于短程自旋玻璃和其他具有淬火无序的材料模型的低温行为的基本问题。严谨和启发式的数学方法将被应用于分析相变的推测存在；纯相和基态的多样性、结构和组织；小磁场的作用；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，被称为自旋玻璃。该项目的重要性在于，这些技术在理论计算机科学或生物学等领域具有广泛的潜在应用，这些领域结合了复杂性和优化问题。这类问题的例子是航空公司的最优路线调度和预测蛋白质的几何结构（从而预测生物功能）。

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.