A universal order parameter for Inverse Magnetic Catalysis

Abstract

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 [1], based on a semi-analytic approximation.