Deconfinement in the presence of a strong magnetic background: An exercise within the MIT bag model

We study the effect of a very strong homogeneous magnetic field B on the thermal deconfinement transition within the simplest phenomenological approach: the MIT bag pressure for the quark-gluon plasma and a gas of pions for the hadronic sector. Even though the model is known to be crude in numerical precision and misses the correct nature of the (crossover) transition, it provides a simple setup for the discussion of some subtleties of vacuum and thermal contributions in each phase, and should provide a reasonable qualitative description of the critical temperature in the presence of B. We find that the critical temperature decreases, saturating for very large fields.