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arXiv · 1710.05411

A continuum of pure states in the Ising model on a halfplane

Douglas Abraham·Charles M. Newman·Senya Shlosman
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Abstract

We study the homogeneous nearest-neighbor Ising ferromagnet on the right half plane with a Dobrushin type boundary condition --- say plus on the top part of the boundary and minus on the bottom. For sufficiently low temperature $T$, we completely characterize the pure (i.e., extremal) Gibbs states, as follows. There is exactly one for each angle $\theta\in\lbrack-\pi/2,+\pi/2]$; here $\theta$ specifies the asymptotic angle of the interface separating regions where the spin configuration looks like that of the plus (respectively, minus) full-plane state. Some of these conclusions are extended all the way to $T=T_{c}$ by developing new Ising exact solution result -- in particular, there is at least one pure state for each $\theta$.

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Douglas Abraham, Charles M. Newman, Senya Shlosman. 2017-10-15. A continuum of pure states in the Ising model on a halfplane. https://doi.org/10.1007/s10955-017-1918-4

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