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We discuss one-loop radiatively-induced magnetic moment in four-dimensionalquantum electrodynamics (QED) with anisotropic coupling, and examine variouscases which may be of interest in effective gauge theories of antiferromagnets,whose planar limit coresponds to highly anisotropic QED couplings. We find adifferent scaling with the magnetic field intensity in case there are extrastatistical gauge interactions in the model with spontaneous symmetry breaking.Such a case is encountered in the CP-1 sigma-model sector of effectivespin-charge separated gauge theories of antiferromagnetic systems. Our workprovides therefore additional ways of possible experimental probing of thegauge nature of such systems.Comment: 14 pages Latex, no figure

Radiatively induced magnetic moment in four-dimensional anisotropic quantum electrodynamics in an external magnetic field