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We give optimal bounds for the homogenization of mixtures of two types of ferromagnetic interactions. This is done by characterizing the possible -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.
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Andrea Braides, Leonard Kreutz, Optimal bounds for periodic mixtures of nearest-neighbour ferromagnetic interactions. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 28 (2017), no. 1, pp. 103–117DOI 10.4171/RLM/754