Magnetic correction to the anomalous magnetic moment of electrons

We investigate the leading order correction of anomalous magnetic moment (AMM) to electrons in a weak magnetic field and find that the magnetic correction is negative and magnetic field dependent, indicating a magnetic catalysis effect for the electron gas. In the laboratory, to measure the g ? 2, the magnitude of the magnetic field B is several T, and correspondingly the magnetic correction to the AMM of electron/muon is around 10^?34/10^?42, therefore the magnetic correction can be safely neglected in the current measurement. However, when the magnitude of the magnetic field strength is comparable with the electron mass, the magnetic correction of the electron's AMM will become considerable. This general magnetic correction to the charged fermion's AMM can be extended to study quantum chromodynamic matter under a strong magnetic field.