The behavior of the quark condensates at zero chemical potential and finite temperature subject to an external magnetic field is studied within the three flavor Nambu–Jona-Lasinio model with Polyakov loop (PNJL) and its extension, the so-called entangled PNJL model (EPNJL). A comparison with recent lattice QCD data is performed and it is shown that at $T=0\mathrm{MeV}$ the light quark condensates are in quantitative agreement. At finite temperature, although there is an overall reasonable agreement with several lattice results, it is shown that in the lattice calculations the effect due to the electric charge quark difference is stronger and the restoration of the $u$ quark chiral symmetry starts at lower temperatures. When considering the entangled PNJL model with a Polyakov loop scale parameter that depends on the magnetic field, it is possible to obtain an earlier rise of the Polyakov loop with the increase of the magnetic field and due to the entanglement, the inverse magnetic catalysis is found as in the lattice QCD calculations.

• Received 17 May 2013
• Corrected 15 January 2014

DOI:https://doi.org/10.1103/PhysRevD.89.016002