Mathematical Sciences: The Mathematics and Physics of Disordered Materials

两位共同首席调查员将研究许多问题 与无序的材料相联系。 物理事件将是 研究包括无阻键随机磁体，无序 电子系统和自旋玻璃。 分析 相应的数学模型预计将导致 关于这些事件的基本发现， 自旋玻璃的温度特性。 数学模型 使用的模型包括渗流模型和经典输运模型， 随机增长模型 大多数问题都与 平衡性质，但有些与动力学有关。 行为 在相变附近将特别感兴趣。 的 这个项目的新奇是严格的研究，主要是植根于 在数学中，通常研究的系统 实验性的 调查人员已经非常 对该领域的宝贵贡献，包括 Cayley树上Ising模型的自旋玻璃相。

The two co-principal investigators will study many problems connected with disordered materials. The physical events to be studied include unfrustrated bond random magnets, disordered electronic systems and spin glasses. Analysis of the corresponding mathematical models is expected to lead to fundamental discoveries about these events such as low temperature properties of spin glasses. The mathematical models used include percolation and classical transport models, and stochastic growth models. Most of the questions relate to the equilibrium properties but some relate to the dynamics. Behavior near the phase transitions will be of particular interest. The novelty of this project is the rigorous study, rooted primarily in mathematics, of systems that are generally studied experimentally. The investigators have already made very valuable contributions to the field including the existence of a spin-glass phase for an Ising model on a Cayley tree.