Static ferromagnetic materials: from the microscopic to the mesoscopic scale

Thanks to averaging processes and Gamma-convergence techniques, we are able to link a microscopic description of ferromagnetic materials based on spin lattices and their mesoscopic description in the static framework for the three fundamental contributions, exchange, magnetostatic and external field. The results are in accordance with the classical continuous description of ferromagnetic phenomena and justifies it. This work is a seed towards a dynamic description of ferromagnetic materials.

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Communications in Contemporary Mathematics, 16(1), 1350013:1–24 (2014)