Abstract
The anomalous magnetic moment (AMM) for excited states of an electron in a constant magnetic field has been calculated within the framework of two-dimensional electrodynamics. The analytical results for the interaction energy of the anomalous magnetic moment with the external magnetic field are obtained in two limiting cases of nonrelativistic and relativistic energy values in a comparatively weak magnetic field. It is shown that the interaction energy of the spin with the external field does not contain infrared divergence and tends to zero as magnetic field decreases, while the electron's AMM increases logarithmically.
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