Abstract
We discuss one-loop radiatively-induced magnetic moment in four-dimensional quantum electrodynamics (QED) with anisotropic coupling, and examine various cases that may be of interest in effective gauge theories of antiferromagnets, whose planar limit corresponds 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 ${\mathrm{CP}}^{1}$ $\ensuremath{\sigma}\ensuremath{-}\mathrm{model}$ 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.
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