Radiatively-induced Magnetic moment in four-dimensional anisotropic QED in an external magnetic field

We discuss one-loop radiatively-induced magnetic moment in four-dimensional quantum electrodynamics (QED) with anisotropic coupling, and examine various cases which may be of interest in effective gauge theories of antiferromagnets, whose planar limit coresponds to highly anisotropic QED couplings. We find a different scaling with the magnetic field intensity in case there are extra statistical gauge interactions in the model with spontaneous symmetry breaking. Such a case is encountered in the CP-1 sigma-model sector of effective spin-charge separated gauge theories of antiferromagnetic systems. Our work provides therefore additional ways of possible experimental probing of the gauge nature of such systems.