论文标题
交互作用 - 面和一致性以面值为中心的立方体
Interaction-round-a-face and consistency-around-a-face-centered-cube
论文作者
论文摘要
统计力学的可集成晶格模型与满足多维一致性的离散集成方程之间存在对应关系，其中后者可以在前者的准经典扩展中找到。本文将此对应关系扩展到相互作用-A-FACE（IRF）模型，从而导致了一致性AROUND-A-CUBE（CAC）的集成性条件的新公式，适用于方形晶格中的五点方程。这些方程式的多维一致性被表述为一致性偏心的以中为中心的立方体（CAFCC），即涉及满足面部中心单位细胞上八个未知变量的14个五点晶格方程的过度确定系统。来自IRF模型的准经典极限，这些限制是根据与Adler-Bobenko-Suris（ABS）列表相关的Star-Triangle关系的连续自旋解构建的，获得了15组方程组，这些方程式满足CAFCC。
There is a correspondence between integrable lattice models of statistical mechanics and discrete integrable equations which satisfy multidimensional consistency, where the latter may be found in a quasi-classical expansion of the former. This paper extends this correspondence to interaction-round-a-face (IRF) models, resulting in a new formulation of the consistency-around-a-cube (CAC) integrability condition applicable to five-point equations in the square lattice. Multidimensional consistency for these equations is formulated as consistency-around-a-face-centered-cube (CAFCC), which namely involves satisfying an overdetermined system of fourteen five-point lattice equations for eight unknown variables on the face-centered cubic unit cell. From the quasi-classical limit of IRF models, which are constructed from the continuous spin solutions of the star-triangle relations associated to the Adler-Bobenko-Suris (ABS) list, fifteen sets of equations are obtained which satisfy CAFCC.
