  We investigate the quantum corrections of the anomalous magnetic moment (AMM)
for fermions in the presence of a strong magnetic field using the Ritus's
approach. At strong fields the particles get different AMM's depending on the
LL's. This result is different from what is obtained with the Schwinger's
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.
