# Local and global geometry of the 2D Ising interface in critical pre-wetting

@article{Ganguly2020LocalAG, title={Local and global geometry of the 2D Ising interface in critical pre-wetting}, author={Shirshendu Ganguly and Reza Gheissari}, journal={arXiv: Probability}, year={2020} }

Consider the Ising model at low-temperatures and positive external field $\lambda$ on an $N\times N$ box with Dobrushin boundary conditions that are plus on the north, east, and west boundaries and minus on the south boundary. If $\lambda = 0$, the interface separating the plus and minus phases is diffusive, having $O(\sqrt N)$ height fluctuations, and the model is fully wetted. Under an order one field, the interface fluctuations are $O(1)$ and the interface is only partially wetted, being…

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