Mathematical Sciences: Exact Analysis of Lattice Statistics Models and Applications

在该项目中，主要研究人员将继续研究手性 Potts 模型中 Yang-Baxter 方程的新的更高属解。 这些解决方案描述了可通过实验实现的系统中的相变，并且它们充当各种普遍性类别的代表。 此外，主要研究人员还将研究不规则晶格上Z不变非齐次Ising模型的自旋相关函数，以获得某些准晶体和某些准周期Ising晶格的相关函数。 统计力学模型是提高我们对晶体等有序结构的理解的重要工具。 此外，对手性波茨模型等模型的研究涉及数学和物理之间的良好相互作用，有助于增强这两个领域。 在这个项目中，主要研究人员将寻找描述准晶体和准周期晶格的杨-巴克斯特方程的新解。 这项工作涉及数学和物理学之间的其他主题，例如量子群和结理论、单极子和弦理论、凝聚态物质的相变以及生物物理学中的生物膜。

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.