QCD phase diagram in the presence of an external magnetic field

The existence of a strong magnetic field (eB) in heavy ion
collisions (HIC) is established through different experiments like
Relativistic Heavy Ion Collider and Large Hadron Collider. A strong
magnetic field is also supposed to exist in a dense object like a
magnetar. Thus, understanding quantum chromodynamics (QCD), which is
essential to understand HICs and neutron stars, in the presence of a
magnetic field is of great importance. In this talk, I will discuss the
QCD phase diagram in the temperature (T) - magnetic field (T-eB) plane
using effective models. I will specifically focus on the effects of
magnetic catalysis (MC) and inverse MC (IMC). I will elaborate on how such
properties can help fix model parameters. The role played by the pion mass
in getting the IMC effect will also be demonstrated. Finally, I discuss
how the phase diagram modifies if the QCD matter behaves as a nonextensive
medium.