论文标题
铁电模型的纯状态的不存在和独特性
Nonexistence and Uniqueness for Pure States of Ferroelectric Six-Vertex Models
论文作者
论文摘要
在本文中，我们考虑了一般的铁电六个vertex模型的纯状状态的存在和独特性。首先，我们证明有一个开放子集$ \ mathfrak {h} \ subset [0，1]^2 $，该区域由两个显式双曲线之间的区域进行了参数化，因此任何slope $（s，s，t）\ in \ mathfrak in \ mathfrak in \ in \ m mathfrak in \ in \ mathfrak n \ in \ h h h h h h h h h hh h} $ nynectric六vertex模型均无纯粹的状态。其次，我们表明，对于$ \ mathfrak {h h} $的边界$ \ partial \ mathfrak {h} $的任何坡度$（s，t）$的模型都有一个独特的纯状态。这些结果证实了1995年布克曼近地区的预测。
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.
