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.
Categories: math.PR math-ph math.MP