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Rendiconti Lincei - Matematica e Applicazioni
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Published online: 2017-03-02
Optimal bounds for periodic mixtures of nearest-neighbour ferromagnetic interactions
Andrea Braides[1] and Leonard Kreutz[2] (1) Università di Roma Tor Vergata, Italy(2) Gran Sasso Science Institute, L’Aquila, Italy
We give optimal bounds for the homogenization of mixtures of two types of ferromagnetic interactions. This is done by characterizing the possible $\Gamma$-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.
Keywords: Spin systems, homogenization, optimal design, $\gamma$-convergence, conducting networks
Braides Andrea, Kreutz Leonard: Optimal bounds for periodic mixtures of nearest-neighbour ferromagnetic interactions. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 28 (2017), 103-117. doi: 10.4171/RLM/754