Dobrushin interfaces via the reflection positivity method

Since the seminal work of Dobrushin, it is now a well known fact that the interface between the two phases of 3D Ising model becomes rigid at low temperatures, in the sense that it deviates only locally from a perfect hyperplane. It appears that some models with infinitely degenerated ground states exhibit these rigid interfaces as well. This new result is a first step towards the conjectured existence of non translation-invariant Gibbs measures for some particular models with continuous symmetry. I will present a general method based on correlation inequalities to get such results.