Optimal bounds for periodic mixtures of nearestneighbour ferromagnetic interactions

We give optimal bounds for the homogenization of mixtures of two types of ferromagnetic interactions. This is done by characterizing the possible G-limits of the corresponding energies in a discrete-to-continuum setting. We show that for nearest-neighbour systems this characterization can be provided by a description of the possible limit Wulff shapes in terms of the percentage of one of the two types of interactions.