Lattice-Statistical Models and Applications

9313648吴这项续期补助金涉及统计力学中晶格模型的理论研究，重点放在准确的结果和应用上。晶格模型保留了真实系统的基本物理特性，在材料研究中至关重要。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、渗流、定向聚合物和膜转变到高温超导体等广泛的物理现象。此外，格子模型研究的结果将被应用于分析结的数学理论中的几个长期悬而未决的问题。%*

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. %%% ***