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Recently, first-order phase transitions have been predicted as an effect ofthe inclusion of quark anomalous magnetic moment (AMM) in the hot andmagnetized Nambu--Jona-Lasinio model (NJL). These transitions appear in thechiral condensate for different combinations of AMM and magnetic fields andcould lead to inverse magnetic catalysis. However, in this work, we show thatthe predicted first-order phase transitions are related toregularization-dependent issues. To show this, we explore, in the context ofthe vacuum magnetic regularization (VMR) scheme, two different scenarios: whenmass-dependent (MD) and mass-independent (MI) terms are present in thesubtraction of the divergences. In the MD case, as we increase the AMM value,it is observed the appearance of a nonmassive minimum in the thermodynamicalpotential, which induces a first-order phase transition from the massiveminimum. We argue that the MD terms must be avoided in order to satisfy thepredictions of Lattice QCD, and we propose a MI solution that is valid in thelimit which the magnetic fields are smaller than the squared of vacuumeffective quark mass.

Artificial first-order phase transition in a magnetized Nambu--Jona-Lasinio model with a quark anomalous magnetic moment