Absence of Dobrushin states for 2d long-range Ising models
Publication date
2018-09
Authors
Coquille, Loren
van Enter, Aernout C.D.
Le Ny, Arnaud
Ruszel, Wioletta M.
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Document Type
Article
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Abstract
We consider the two-dimensional Ising model with long-range pair interactions of the form Jxy∼|x−y|−α with α>2 , mostly when Jxy≥0 . We show that Dobrushin states (i.e. extremal non-translation-invariant Gibbs states selected by mixed ± 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.
Keywords
Gibbs states, Long-range Ising model, Dobrushin states, Interface fluctuations
Citation
Coquille, L, van Enter, A C D, Le Ny, A & Ruszel, W M 2018, 'Absence of Dobrushin states for 2d long-range Ising models', Journal of Statistical Physics, vol. 172, no. 5, pp. 1210-1222. https://doi.org/10.1007/s10955-018-2097-7