The localisation of low-temperature interfaces in d dimensional Ising model
Résumé
We study the Ising model in a box Λ in Z^d (not necessarily parallel to the directions of the lattice) with Dobrushin boundary conditions at low temperature. We couple the spin configuration with the configurations under + and − boundary conditions and we define the interface as the edges whose endpoints have the same spins in the + and − configurations but different spins with the Dobrushin boundary conditions. We prove that, inside the box Λ, the interface is localized within a distance of order ln^2 |Λ| of the set of the edges which are connected to the top by a + path and connected to the bottom by a − path.
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