Mathematical Sciences: Exact Analysis of Lattice-Statistics Models and Applications to Biomembranes

Perk教授、Au-Yang教授和Scott教授将研究 统计力学中的可解二维模型 在 特别是，他们将研究的高亏格解决方案 手征Potts模型中的Yang-Baxter方程。 此外，他们还将研究自旋-自旋关联函数 不规则环上的Z不变非齐次伊辛模型 晶格 手性Potts模型的精确结果将是： 通过斯科特和皮尔斯的模型应用于生物膜。 这项工作有望增加新的深入了解 “涟漪”阶段，发生在生物膜中。 该项目是一个跨学科的项目， 数学物理、凝聚态理论和生物物理。 数学和统计力学的相互作用 纯数学在纽结等领域的新发展 理论和theta函数理论。 精确的研究 在凝聚态物质中， 阐明生物膜的主题， 直接进入计算。

Professors Perk, Au-Yang, and Scott will study exactly soluble two dimensional models in statistical mechanics. In particular, they will investigate the higher genus solutions of the Yang-Baxter equations in the chiral Potts model. Furthermore, they will study the spin-spin correlation functions of the Z-invariant inhomogeneous Ising model on an irregular lattice. The exact results in the chiral Potts model will be applied to biomembranes through the model of Scott and Pearce. This work promises to add new in-depth understanding of the "ripple" phase which occurs in biomembranes. This project is an interdisciplinary one involving mathematical physics, condensed matter theory, and biophysics. The interplay of mathematics and statistical mechanics could lead to new developments in pure mathematics in areas such as knot theory and the theory of theta functions. The study of exactly soluble two dimensional models in condensed matter could illuminate the subject of biomembranes in areas which are not directly accessible to computations.