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Rendiconti Lincei - Matematica e Applicazioni


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Volume 28, Issue 1, 2017, pp. 103–117
DOI: 10.4171/RLM/754

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