  We study dynamical chiral symmetry breaking for quarks in the fundamental
representation of $SU(N_c)$ for $N_f$ number of light quark flavors. We also
investigate the phase diagram of quantum chromodynamics at finite temperature
$T$ and/or in the presence of a constant external magnetic field $eB$. The
unified formalism for this analysis is provided by a symmetry-preserving
Schwinger-Dyson equations treatment of a vector$\times$vector contact
interaction model which encodes several well-established features of quantum
chromodynamics to mimic the latter as closely as possible. Deconfinement and
chiral symmetry restoration are triggered above a critical value of $N_f$ at
$T=0=eB$. On the other hand, increasing temperature itself screens strong
interactions, thus ensuring that a smaller value of $N_f$ is sufficient to
restore chiral symmetry at higher temperatures. We also observe the well-known
phenomenon of magnetic catalysis for a strong enough magnetic field. However,
we note that if the effective coupling strength of the model decreases as a
function of magnetic field, it can trigger inverse magnetic catalysis in a
certain window of this functional dependence. Our model allows for the
simultaneous onset of dynamical chiral symmetry breaking and confinement for
each case. Qualitative as well as quantitative predictions of our simple but
effective model are in reasonably satisfactory agreement with lattice results
and other reliable and refined predictions based upon intricate continuum
studies of quantum chromodynamics.
