  In this paper, we study the influence of an external magnetic field in
holographic QCD models where the backreaction is modeled in via an appropriate
choice of the background metric. We add a phenomenological soft wall dilaton to
incorporate better IR behavior (confinement). Elaborating on previous studies
conducted by [JHEP 1505 (2015) 121], we first discuss the Hawking-Page
transition, the dual of the deconfinement transition, as a function of the
magnetic field. We confirm that the critical deconfinement temperature can drop
with the magnetic field. Secondly, we study the quark condensate
holographically as a function of the applied magnetic field and demonstrate
that this model does not exhibit inverse magnetic catalysis at the level of the
chiral transition. The quest for a holographic QCD model that qualitatively
describes the inverse magnetic catalysis at finite temperature is thus still
open. Throughout this work, we pay special attention to the different
holographic parameters and we attempt to fix them by making the link to genuine
QCD as close as possible. This leads to several unanticipated and so far
overlooked complications (such as the relevance of an additional length scale
in the confined geometry) that we discuss in detail.
