# Nonexistence and Uniqueness for Pure States of Ferroelectric Six-Vertex Models

@article{Aggarwal2020NonexistenceAU, title={Nonexistence and Uniqueness for Pure States of Ferroelectric Six-Vertex Models}, author={A. Aggarwal}, journal={arXiv: Probability}, year={2020} }

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… Expand

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