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In this paper, we study the influence of an external magnetic field inholographic QCD models where the backreaction is modeled in via an appropriatechoice of the background metric. We add a phenomenological soft wall dilaton toincorporate better IR behavior (confinement). Elaborating on previous studiesconducted by [JHEP 1505 (2015) 121], we first discuss the Hawking-Pagetransition, the dual of the deconfinement transition, as a function of themagnetic field. We confirm that the critical deconfinement temperature can dropwith the magnetic field. Secondly, we study the quark condensateholographically as a function of the applied magnetic field and demonstratethat this model does not exhibit inverse magnetic catalysis at the level of thechiral transition. The quest for a holographic QCD model that qualitativelydescribes the inverse magnetic catalysis at finite temperature is thus stillopen. Throughout this work, we pay special attention to the differentholographic parameters and we attempt to fix them by making the link to genuineQCD as close as possible. This leads to several unanticipated and so faroverlooked complications (such as the relevance of an additional length scalein the confined geometry) that we discuss in detail.

No inverse magnetic catalysis in the QCD hard and soft wall models