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 ba
re 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 strenght of the magnetic field, and it is capable to capture both the deconfinement crossover and the chiral crossover. Besides, we compute self-consistently 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, $eB=19 m_pi^2$, the split is of the order of $10%$. A qualitative comparison with other effective models and recent Lattice results is also performed.
We study the two-flavor Nambu--Jona-Lasinio model with the Polyakov loop (PNJL model) in the presence of a strong magnetic field and a chiral chemical potential $mu_5$ which mimics the effect of imbalanced chirality due to QCD instanton and/or sphale
ron transitions. Firstly we focus on the properties of chiral symmetry breaking and deconfinement crossover under the strong magnetic field. Then we discuss the role of $mu_5$ on the phase structure. Finally the chirality charge, electric current, and their susceptibility, which are relevant to the Chiral Magnetic Effect, are computed in the model.
