We perform a model study of deconfinement and chiral symmetry restoration in a strong magnetic background .
We use a Nambu-Jona Lasinio model with the Polyakov loop , taking into account a possible dependence of the coupling on the Polyakov loop expectation value , as suggested by the recent literature .
Our main result is that , within this model , the deconfinement and chiral crossovers of QCD in strong magnetic field are entangled even at the largest value of eB considered here , namely eB = 30 m _ { \pi } ^ { 2 } ( that is , B \approx 6 \times 10 ^ { 15 } Tesla ) .
The amount of split that we measure is , at this value of eB , of the order of 2 \% .
We also study briefly the role of the 8-quark term on the entanglement of the two crossovers .
We then compare the phase diagram of this model with previous results , as well as with available Lattice data .