Absence of Dobrushin States for 2d Long-Range Ising Models

Loren Coquille*, Aernout C.D. van Enter, Arnaud Le Ny, Wioletta M. Ruszel

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

7 Citations (Scopus)
32 Downloads (Pure)


We consider the two-dimensional Ising model with long-range pair interactions of the form (Formula presented.) with (Formula presented.), mostly when (Formula presented.). 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 languageEnglish
Pages (from-to)1210-1222
Number of pages13
JournalJournal of Statistical Physics
Publication statusPublished - 2018

Bibliographical note

Accepted Author Manuscript


  • Dobrushin states
  • Gibbs states
  • Interface fluctuations
  • Long-range Ising model


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