TY - JOUR
T1 - Absence of Dobrushin States for 2d Long-Range Ising Models
AU - Coquille, Loren
AU - van Enter, Aernout C.D.
AU - Le Ny, Arnaud
AU - Ruszel, Wioletta M.
N1 - Accepted Author Manuscript
PY - 2018
Y1 - 2018
N2 - 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.
AB - 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.
KW - Dobrushin states
KW - Gibbs states
KW - Interface fluctuations
KW - Long-range Ising model
UR - http://www.scopus.com/inward/record.url?scp=85049149032&partnerID=8YFLogxK
UR - http://resolver.tudelft.nl/uuid:e034ebd5-467a-4a44-9948-43a7ed7690bd
U2 - 10.1007/s10955-018-2097-7
DO - 10.1007/s10955-018-2097-7
M3 - Article
AN - SCOPUS:85049149032
SN - 0022-4715
VL - 172
SP - 1210
EP - 1222
JO - Journal of Statistical Physics
JF - Journal of Statistical Physics
ER -