Mathematical Sciences: Exact Analysis of Lattice Statistics Models and Applications

在这个项目中，主要研究人员将继续 他们对杨-巴克斯特方程的新的更高亏格解的研究 手性Potts模型中的方程。 这些解决方案描述了 实验上可实现的系统中的相变， 作为各种普遍性类别的代表。 在 此外，主要研究人员将研究自旋-自旋 Z不变非齐次Ising的相关函数 模型上的不规则晶格，以获得相关性 某些准晶和某些准周期伊辛函数 格子 统计力学中的模型是 提高我们对有序结构的理解， 晶体 此外，对像手征波茨模型的研究 模型包含了数学和物理之间的良好互动 这有助于增强这两个领域。 本工程 主要研究人员将寻找新的解决方案的杨- 描述准晶和准周期的巴克斯特方程 格子 这项工作涉及边境的其他主题 数学和物理之间的联系比如量子群和纽结 理论，单极子和弦理论，相变 生物物理学中的凝聚态物质和生物膜。

In this project the principal investigators will continue their study of new, higher-genus solutions of the Yang-Baxter equation in the chiral Potts model. These solutions describe phase transitions in experimentally realizable systems and they serve as representatives of various universality classes. In addition, the principal investigators will look at spin-spin correlation functions of the Z-invariant inhomogeneous Ising model on an irregular lattice, in order to obtain the correlation functions of certain quasicrystals and some quasiperiodic Ising lattices. Models in statistical mechanics are an important vehicle for improving our understanding of ordered structures such as crystals. In addition, the study of models like the chiral Potts model involves a nice interplay between mathematics and physics that serves to enhance both fields. In this project the principal investigators will look for new solutions of the Yang- Baxter equation that describe quasicrystals and quasiperiodic lattices. This work touches upon other topics on the border between mathematics and physics such as quantum groups and knot theory, monopoles and string theory, phase transitions in condensed matter and biomembranes in biophysics.