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.
Original language | English |
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Pages (from-to) | 1210-1222 |
Number of pages | 13 |
Journal | Journal of Statistical Physics |
Volume | 172 |
Issue number | 5 |
DOIs | |
Publication status | Published - Sept 2018 |
Externally published | Yes |
Keywords
- Gibbs states
- Long-range Ising model
- Dobrushin states
- Interface fluctuations