The localisation of low-temperature interfaces in d dimensional Ising model

Wei Zhou (1, 2)

1 UP11 - Université Paris-Sud - Paris 11
2 DMA - Département de Mathématiques et Applications - ENS Paris

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.

Domaines: Probabilités [math.PR]

Wei Zhou. The localisation of low-temperature interfaces in d dimensional Ising model. 2019. ⟨hal-02100895⟩