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Using two different models from holographic quantum chromodynamics (QCD) westudy the deconfinement phase transition in $2+1$ dimensions in the presence ofa magnetic field. Working in 2+1 dimensions lead us to {\sl exact} solutions onthe magnetic field, in contrast with the case of 3+1 dimensions where thesolutions on the magnetic field are perturbative. As our main result we predicta critical magnetic field $B_c$ where the deconfinement critical temperaturevanishes. For weak fields meaning $B<B_c$ we find that the critical temperaturedecreases with increasing magnetic field indicating an inverse magneticcatalysis (IMC). On the other hand, for strong magnetic fields $B>B_c$ we findthat the critical temperature raises with growing field showing a magneticcatalysis (MC). These results for IMC and MC are in agreement with theliterature.

Deconfinement phase transition in a magnetic field in 2+1 dimensions from holographic models