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arXiv · 1804.04889

Absence of Dobrushin states for $2d$ long-range Ising models

Loren Coquille·Aernout C. D. van Enter·Arnaud Le Ny·Wioletta M. Ruszel
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Abstract

We consider the two-dimensional Ising model with long-range pair interactions of the form $J_{xy}\sim|x-y|^{-\alpha}$ with $\alpha>2$, mostly when $J_{xy} \geq 0$. We show that Dobrushin states (i.e. extremal non-translation-invariant Gibbs states selected by mixed $\pm$-boundary conditions) do not exist. We discuss possible extensions of this result in the direction of the Aizenman-Higuchi theorem, or concerning fluctuations of interfaces. We also mention the existence of rigid interfaces in two long-range anisotropic contexts.

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Loren Coquille, Aernout C. D. van Enter, Arnaud Le Ny, Wioletta M. Ruszel. 2018-04-13. Absence of Dobrushin states for $2d$ long-range Ising models. https://doi.org/10.1007/s10955-018-2097-7

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