Magnetic catalysis and inverse magnetic catalysis in (2+1)-dimensional gauge theories from holographic models

We study the deconfinement phase transition in $(2+1)$-dimensional holographic $SU(N)$ gauge theories in the presence of an external magnetic field from the holographic hard and soft wall models. We obtain exact solutions for the critical temperature of the deconfinement transition for any range of magnetic field. As a consequence, we find a critical magnetic field $(B_c)$, in which the critical temperature $(T_c)$ vanishes; for $B<B_c$ we have an inverse magnetic catalysis and for $B>B_c$ we have a magnetic catalysis.