Mathematical Sciences: The Mathematics and Physics of Disordered Materials

两位联合首席调查员将研究与无序材料有关的许多问题。要研究的物理事件包括未受挫的键随机磁铁、无序电子系统和自旋玻璃。对相应数学模型的分析有望导致对这些事件的基本发现，如自旋玻璃的低温性质。所使用的数学模型包括渗流模型和经典输运模型，以及随机增长模型。大多数问题与平衡性质有关，但也有一些与动力学有关。相变附近的行为将特别令人感兴趣。这个项目的新奇之处在于对通常通过实验研究的系统进行了严格的研究，这些研究主要植根于数学。研究人员已经在这一领域做出了非常有价值的贡献，包括在Cayley树上的伊辛模型中存在自旋玻璃相。

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.