  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.
