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 ${\mu }_c(B)$ acts as an order parameter to distinguish Inverse Magnetic Catalysis from Magnetic Catalysis. Moreover, we propose a universal relation between ${\mu }_c(B)$ 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 $\mu$, 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 [JHEP 1103 (2011) 033], based on a semi-analytic approximation.