铁电六顶点模型纯态的不存在性和唯一性
Nonexistence and Uniqueness for Pure States of Ferroelectric Six-Vertex Models
摘要：
本文研究了一般铁电六顶点模型中具有固定斜率$(s, t) \in [0, 1]^2$的纯态的存在唯一性。首先，我们证明了存在一个开子集$\mathfrak{H} \subset [0, 1]^2$，它由两个显式双曲线之间的区域参数化，使得任何斜率的铁电六顶点模型$(s, t) \in \mathfrak{H}$都不存在纯态。其次，我们证明了对于任何斜率的$(s, t)$模型，在$\mathfrak{H}$的边界$\partial \mathfrak{H}$上存在唯一的纯态。这些结果证实了Bukman-Shore在1995年的预测。
英文摘要：
In this paper we consider the existence and uniqueness of pure states with some fixed slope $(s, t) \in [0, 1]^2$ for a general ferroelectric six-vertex model. First, we show there is an open subset $\mathfrak{H} \subset [0, 1]^2$, which is parameterized by the region between two explicit hyperbolas, such that there is no pure state for the ferroelectric six-vertex model of any slope $(s, t) \in \mathfrak{H}$. Second, we show that there is a unique pure state for this model of any slope $(s, t)$ on the boundary $\partial \mathfrak{H}$ of $\mathfrak{H}$. These results confirm predictions of Bukman-Shore from 1995.
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