  Lattice simulations have demonstrated that a background (electro)magnetic
field reduces the chiral/deconfinement transition temperature of quantum
chromodynamics for eB < 1 GeV^2. On the level of observables, this reduction
manifests itself in an enhancement of the Polyakov loop and in a suppression of
the light quark condensates (inverse magnetic catalysis) in the transition
region. In this paper, we report on lattice simulations of 1+1+1-flavor QCD at
an unprecedentedly high value of the magnetic field eB = 3.25 GeV^2. Based on
the behavior of various observables, it is shown that even at this extremely
strong field, inverse magnetic catalysis prevails and the transition, albeit
becoming sharper, remains an analytic crossover. In addition, we develop an
algorithm to directly simulate the asymptotically strong magnetic field limit
of QCD. We find strong evidence for a first-order deconfinement phase
transition in this limiting theory, implying the presence of a critical point
in the QCD phase diagram. Based on the available lattice data, we estimate the
location of the critical point.
