Print Email Facebook Twitter Absence of Dobrushin States for 2d Long-Range Ising Models Title Absence of Dobrushin States for 2d Long-Range Ising Models Author Coquille, Loren (Université Grenoble Alpes) van Enter, A.C.D. (Rijksuniversiteit Groningen) Le Ny, Arnaud (Université Paris-Est; Eindhoven University of Technology) Ruszel, W.M. (TU Delft Applied Probability) Date 2018 Abstract 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. Subject Dobrushin statesGibbs statesInterface fluctuationsLong-range Ising model To reference this document use: http://resolver.tudelft.nl/uuid:e034ebd5-467a-4a44-9948-43a7ed7690bd DOI https://doi.org/10.1007/s10955-018-2097-7 Embargo date 2019-06-01 ISSN 0022-4715 Source Journal of Statistical Physics, 172, 1210-1222 Bibliographical note Accepted Author Manuscript Part of collection Institutional Repository Document type journal article Rights © 2018 Loren Coquille, A.C.D. van Enter, Arnaud Le Ny, W.M. Ruszel Files PDF 45659044_interfacesstates.pdf 423.08 KB Close viewer /islandora/object/uuid:e034ebd5-467a-4a44-9948-43a7ed7690bd/datastream/OBJ/view