Equilibrium and ageing in glassy systems

这些项目旨在研究高度无序系统的平衡和动力学性质，如自旋玻璃。在这类系统中，平衡态在热力学极限下表现为Gibbs态的复杂结构，而动力学则表现为向局部响应的缓慢瞬变。导致“老龄化”现象的全球均衡。我们计划在一类具有层次关联的高斯自旋玻璃中研究这些特征之间的关系，即所谓的广义随机能量模型。在这些模型中，我们期望获得对吉布斯措施的完整描述。在此基础上，我们计划研究与之相关的随机动力学的更困难的问题。这个问题以前已经在最简单的例子--随机能量模型中得到了解决，我们希望在此背景下开发的方法将为在更复杂的情况下进行分析提供基础。

The projects aims at the investigation of equilibrium and dynamical properties of highly disordered systems such as spin glasses. In such systems the equilibrium is characterized by a complex structure of the Gibbs states in the thermodynamic limit, while the dynamics are characterized by slow transients towards local resp. global equilibria that give rise to the `ageing' phenomenon. We plan to investigate the relation between these features within a class of Gaussian spin glasses with hierarchical correlations, the so-called Generalised Random Energy Models. In these models we expect to obtain a full description of the Gibbs measures. On this basis we then plan to investigate the much harder problem of the associated stochastic dynamics. This problem has been solved previously in the simplest example, the Random Energy Model, and we expect the methods developed in this context to provide a basis for the analysis in more complex situations.