Phase transitions in layered systems

Abstract

We consider the Ising model on the two-dimensional square lattice where on each horizontal line, called "layer", the interaction is given by a ferromagnetic Kac potential with coupling strength $J_{\gamma }(x,y)=\gamma J(\gamma (x-y))$, where $J(\cdot )$ is smooth and has compact support; we then add a nearest neighbor ferromagnetic vertical interaction of strength ${\gamma }^A$ (where $A\ge 2$ is fixed) and prove that for any $\beta$ (inverse temperature) larger than the mean field critical value there is a phase transition for all $\gamma$ small enough.

17 pages. Final version. Published in Journal of Statistical Physics (2014), volume 157, 407-421