We evaluate the dressed Polyakov loop for hot quark matter in strong magnetic field. To compute the finite temperature effective potential, we use the Polyakov extended Nambu–Jona-Lasinio model with eight-quark interactions taken into account. The bare quark mass is adjusted in order to reproduce the physical value of the vacuum pion mass. Our results show that the dressed Polyakov loop is very sensitive to the strength of the magnetic field, and it is capable to capture both the deconfinement crossover and the chiral crossover. Additionally, we self-consistently compute the phase diagram of the model. We find a tiny split of the two aforementioned crossovers as the strength of the magnetic field is increased. Concretely, for the largest value of magnetic field investigated here, $eB=19m_{\pi }^2$, the split is of the order of 10%. A qualitative comparison with other effective models and recent lattice results is also performed.

• Received 11 July 2010

DOI:https://doi.org/10.1103/PhysRevD.82.054027