Lattice-Statistical Models and Applications

[9313648]吴：这项更新资助是关于统计力学中晶格模型的理论研究，重点是精确结果和应用。晶格模型保留了真实系统的基本物理性质，在材料研究中是至关重要的。这项研究将包括对几个二维和三维系统的研究，这些系统描述了从吸附、渗透、定向聚合物、膜转变到高温超导体等广泛的物理现象。此外，晶格模型的研究结果将应用于分析结数学理论中几个长期未解决的问题。% % % * * *

9313648 Wu This renewal grant concerns theoretical studies of lattice models in statistical mechanics with emphases on exact results and applications. Lattice models which retain the essential physics of real systems are crucial in materials research. The research will include the study of several two-and three-dimensional systems which describe a wide range of physical phenomena ranging from adsorption, percolation, directed polymers, and membrane transitions, to high temperature superconductors. In addition, results of lattice model studies will be applied to analyze several long-standing unresolved problems in the mathematical theory of knots. %%% ***