A universal order parameter for Inverse Magnetic Catalysis

We revisit the chiral transition in the finite density Sakai-Sugimoto model and find that, at fixed temperature T, the magnetisation near the critical line μ c (B) acts as an order parameter to distinguish Inverse Magnetic Catalysis from Magnetic Catalysis. Moreover, we propose a universal relation between μ c (B) and the magnetisation that allows us to predict the behaviour of the former from the behaviour of the latter. We find that a similar relation holds, at fixed chemical potential μ, for the critical line T c (B). Our results are obtained by investigating a fully numerical solution to the relevant equations. At low temperatures our results reduce to those obtained by Preis, Rebhan and Schmitt [1], based on a semi-analytic approximation.