Hofstadter's diagram (the energy spectrum against the magnetic field in tight-binding systems) is obtained for the models having flat one-electron band(s) that have originally been proposed for itinerant spin ferromagnetism. Magnetic fields preserve those flat bands that arise from a topological reason, while dispersions emerge in a singular manner for the flat bands arising from interference. This implies an anomalous orbital magnetism.
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Aoki et al. (1996) studied this question.
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