Abstract
We derive the field energy of micromagnetics by computing the limiting energy of a lattice of dipoles as a typical lattice parameter goes to zero. Different limiting energies are obtained, depending upon whether the dipoles do not oscillate (strong convergence), oscillate on a scale much larger than the scale of the lattice (weak-long) or oscillate on the scale of the lattice (weak-short). The analysis suggests a framework and some methods for the direct derivation of continuum theory from molecular theory.
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James, R.D., Müller, S. Internal variables and fine-scale oscillations in micromagnetics. Continuum Mech. Thermodyn 6, 291–336 (1994). https://doi.org/10.1007/BF01140633
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DOI: https://doi.org/10.1007/BF01140633