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The problem of tight-binding electrons in a two-dimensional lattice with a magnetic flux p/q in each plaquette is investigated for p=0, 1, 3; q=2, 3, 4, 6, 8. For fixed electron filling, , the total kinetic energy of the electrons has an absolute minimum for one flux quantum per particle, i. e. , when p/q=, where is 1, (1/2, 2 for square, triangular, and honeycomb lattice.
Hasegawa et al. (Mon,) studied this question.