Inserted: 20 oct 2016
Last Updated: 14 jul 2018
Journal: Calc. Var. Partial Diff. Equations
We provide a general framework for the optimal design of surface energies on networks. We prove sharp bounds for the homogenization of discrete systems describing mixtures of ferromagnetic interactions by constructing optimal microgeometries, and we prove a localization principle which allows to reduce to the periodic setting in the general nonperiodic case.