论文标题
晶格模型，差分形式和杨巴克斯特方程
Lattice models, differential forms, and the Yang-Baxter equation
论文作者
论文摘要
我们介绍了新的方法来描述六个vertex和八个vertex晶格模型的统计力学的可允许状态。对于六个Vertex模型，我们将可接受的状态视为网格图上的差异形式。这产生了新的证明，证明了矩形网格的可接受状态与3色之间的对应关系。对于八个Vertex模型，我们将一组可接受的状态解释为$ \ mathbb {f} _2 $ -vector Space。该观点使我们列举了可允许的国家的集合。最后，我们发现杨巴克斯特方程的必要条件可以保留一般的八个vertex模型。
We introduce new methods to describe admissible states of the six-vertex and the eight-vertex lattice models of statistical mechanics. For the six-vertex model, we view the admissible states as differential forms on a grid graph. This yields a new proof of the correspondence between admissible states and 3-colorings of a rectangular grid. For the eight-vertex model, we interpret the set of admissible states as an $\mathbb{F}_2$-vector space. This viewpoint lets us enumerate the set of admissible states. Finally, we find necessary conditions for a Yang-Baxter equation to hold for the general eight-vertex model.
