We investigate the effects of the anomalous magnetic moment (AMM) in the equation of state (EoS) of a system of charged fermions at finite density in the presence of a magnetic field. In the region of strong magnetic fields (eB>m^2) the AMM is found
from the one-loop fermion self-energy. In contrast to the weak-field AMM found by Schwinger, in the strong magnetic field region the AMM depends on the Landau level and decreases with it. The effects of the AMM in the EoS of a dense medium are investigated at strong and weak fields using the appropriate AMM expression for each case. In contrast with what has been reported in other works, we find that the AMM of charged fermions makes no significant contribution to the EoS at any field value.
We investigate the effects of the anomalous magnetic moment (AMM) in the EoS of a fermion system in the presence of a magnetic field. In the region of strong magnetic fields ($B>m^2$) the AMM is found from the one-loop fermion self-energy. In contras
t to the weak-field AMM found by Schwinger, in the strong magnetic field case, the AMM depends on the Landau level (LL) and decreases with it. The effects of the AMM in the EoS at intermediate-to-large fields can be found introducing the one-loop, LL-dependent AMM in the effective Lagrangian that is then used to find the thermodynamic potential of the system. We compare the plots of the parallel and perpendicular pressures versus the magnetic field in the strong field region considering the LL-dependent AMM, the Schwinger AMM, and no AMM at all. The results clearly show a separation between the physical magnitudes found using the Schwinger AMM and the LL-dependent AMM. This is an indication of the inconsistency of considering the Schwinger AMM beyond the weak field region $B< m^2$ where it was originally found. The curves for the EoS, pressures and magnetization at different fields give rise to the well-known de Haas van Alphen oscillations, associated to the change in the number of LL contributing at different fields.
We investigate the quantum corrections of the anomalous magnetic moment (AMM) for fermions in the presence of a strong magnetic field using the Rituss approach. At strong fields the particles get different AMMs depending on the LLs. This result is di
fferent from what is obtained with the Schwingers approximation at weak field where the AMM is independent of the LL. We analyze the significance of the AMM contribution to the Equation of State (EoS) of the magnetized system, in the weak and strong field approximations.
