  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 contrast 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.
