Surface tension and the Ornstein-Zernike behaviour for the 2D

We prove existence of the surface tension in the low temperature 2D Blume-Capel model and verify the Ornstein-Zernike asymptotics of the corresponding finite-volume interface partition function. 1 Setting and results Study of Gibbs states describing an interface between coexisting phases of lattice models goes back to the seminal Dobrushin’s paper [10], where he proved exis-tence of translation noninvariant Gibbs state for the 3-dimensional Ising model. His idea of describing the interface in terms of weakly interacting excitations— walls—separated by “flat regions ” with minimal energy cost—ceilings—was sub-sequently extended to a more general class of models [20] whose pure phases are described by the Pirogov-Sinai theory [27]. Even more general situation arises whenever there is a competition between several different types of ceilings [21]. For these models, the existence of an interface Gibbs state, characterized by overwhelming prevalence of a given type of ceiling, depends on the values of pa-rameters like the temperature, external fields etc. For particular values of these parameters we have coexistence: Gibbs states characterized by different types of ceilings can be constructed as the thermodynamic limit of finite volume states with an appropriately chosen boundary condition. The corresponding phase boundary can be studied using once more the Pirogov-Sinai theory, this time to describe the “gas of walls ” representing the interface. ∗Partly supported by DFG postdoctoral fellowshi