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Antiferromagnetic ground states with abnormal parity characterized by "magnetic" translations are discussed. Their excitations are described by a nonlinear σ-model with the Chern-Simons term with integer ϑ and obey fractional spin and statistics with even denominators. The effective action is derived on the basis of a large N-approximation. The large N reduces the problem to the Hall effect and realizes the parity anomaly.
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Khveshchenko et al. (1989) studied this question.
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