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

Using two different models from holographic quantum chromodynamics (QCD) we study the deconfinement phase transition in 2+1 dimensions in the presence of a magnetic field. Working in 2+1 dimensions lead us to exact solutions on the magnetic field, in contrast with the case of 3+1 dimensions where the solutions on the magnetic field are perturbative. As our main result we predict a critical magnetic field Bc where the deconfinement critical temperature vanishes. For weak fields meaning BBc we find that the critical temperature raises with growing field showing a magnetic catalysis (MC). These results for IMC and MC are in agreement with the literature.