Mathematical Studies of Short-Ranged Spin Glasses

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;和非平衡动力学。brbr该项目的目的是发展数学技术，并在无序材料（称为自旋玻璃）的低温特性的某些特定模型中取得结果。该项目的重要性在于，这些技术具有长期应用的潜力，可以解决理论计算机科学或生物学等领域出现的各种问题，这些问题将复杂性和优化问题联合收割机结合在一起。这类问题的例子是航空公司的最佳路线调度和预测蛋白质的几何结构（从而生物功能）。

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.brbrThe purpose of this project is to develop mathematical techniques and results in certain specific models of the low temperature properties of disordered materials, known as spin glasses. The importance of the project is that these techniques have potential application, over the long term, to a wide range of problems arising 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.