Mathematical Sciences: Classical and Quantum Lattice Systems with Continuous Groups of Symmetry

巴拉班教授将研究具有连续对称群的低温经典和量子自旋系统，特别是经典和量子海森堡模型和哈伯德模型。对于这些模型，他将使用重整化群方法构造一个低温展开式。他将使用这种扩展来证明有关模型的基本事实，例如存在一个具有自发磁化和相关性幂律衰减的纯相连续体。巴拉班教授将要研究的模型是磁性材料的数学模型。最终目标是提供目前缺乏的材料磁性的基本理解。方法是处理越来越接近现实的模型。

Professor Balaban will conduct research on low temperature classical and quantum spin systems with continuous symmetry groups, in particular on the classical and quantum Heisenberg models and the Hubbard model. For these models he will construct a low temperature expansion using the renormalization group approach. He will use this expansion to prove basic facts about the models such as the existence of a continuum of pure phases with spontaneous magnetization and power law decay of correlations. The models which Professor Balaban will investigate are mathematical models of magnetic materials. The ultimate goal is to provide the basic understanding of magnetism in materials which is lacking at the present time. The method is to tackle models which are closer and closer to reality.