论文标题
不均匀的六个vertex模型的一些代数方面
Some Algebraic Aspects of the Inhomogeneous Six-Vertex Model
论文作者
论文摘要
无与伦比的六个vertex模型是2 $ d $多参数集成统计系统。在缩放限制中，预计将涵盖不同类别的临界行为，在大多数情况下，这些行为仍未得到探索。对于参数和扭曲边界条件的一般值，模型具有$ {\ rm u}（1）$不变性。在本文中，我们讨论了对与集成结构一致的其他全局对称性的参数施加的限制。其中包括$ {\ cal c} $，$ {\ cal p} $和$ {\ cal t} $的晶格对应物以及翻译不变性。考虑了具有附加$ {\ cal z} _r $不变性的晶格系统的特殊属性。我们还描述了与可集成的结构相一致的遗传结构。该分析为研究不均匀六个vertex模型的缩放限制奠定了基础。
The inhomogeneous six-vertex model is a 2$D$ multiparametric integrable statistical system. In the scaling limit it is expected to cover different classes of critical behaviour which, for the most part, have remained unexplored. For general values of the parameters and twisted boundary conditions the model possesses ${\rm U}(1)$ invariance. In this paper we discuss the restrictions imposed on the parameters for which additional global symmetries arise that are consistent with the integrable structure. These include the lattice counterparts of ${\cal C}$, ${\cal P}$ and ${\cal T}$ as well as translational invariance. The special properties of the lattice system that possesses an additional ${\cal Z}_r$ invariance are considered. We also describe the Hermitian structures, which are consistent with the integrable one. The analysis lays the groundwork for studying the scaling limit of the inhomogeneous six-vertex model.
