Why stripes? Spontaneous formation of inhomogeneous structures due to elastic interactions

We argue that elastic interactions between ions in different valence states can pla an essential role in the stabilization of stripes (or 2D "sheets") in doped oxides. These interactions are in general long range and anisotropic ( attractive in certain directions and repulsive in others). This can naturally give rise to stripe-like structures in insulating materials. We illustrate this general idea with certain specific examples and show that the situation can be described by the Ising model with anisotropic interactions. The case of anisotropic impurities, relevant, e.g., for manganites, is also briefly discussed.