Dobrushin interfaces via reflection positivity (Q2466829)

For low temperature 3D Ising model an example of a pure state, with a coexistence of phases separated by an interface, was given by \textit{R. L. Dobrushin} [Theory Probab. Appl. 17, 582--600 (1972; Zbl 0275.60119)]. Since then a conjecture has been built that at critical temperature, such system apart from the translation invariant states posesses as well states that are not translation invariant. They are to describe a coexistence of ordered states and a chaotic state, with the rigid interface separating them. The present paper primarily aimed at the proof of this conjecture. This program has not been satisfactorily completed, but a novel method of reflection positivity [this, originally due to \textit{S. Shlosman}, Russ. Math. Surv. 41, 83--134 (1986)] has been adopted to tackle the problem. The method has been proved to work for non-linear sigma models, Ising and Potts models, large entropy systems of continuous spins, with a hope for a generalization for systems with continuous symmetry.