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

巴拉班教授将对具有连续对称群的低温经典和量子自旋系统进行研究，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建低温膨胀。他将利用这个展开式来证明有关模型的基本事实，例如存在具有自发磁化的纯相连续统和关联的幂定律衰变。巴拉班教授将研究的模型是磁性材料的数学模型。最终目的是提供对材料中磁性的基本理解，这是目前所缺乏的。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.