# A universal order parameter for Inverse Magnetic Catalysis

## TL;DR

This paper identifies magnetisation as an order parameter for the chiral transition in the Sakai-Sugimoto model, establishing a universal relation that predicts inverse magnetic catalysis behavior at finite density.

## Contribution

It introduces a universal relation between critical chemical potential and magnetisation, providing a new way to distinguish inverse magnetic catalysis from magnetic catalysis.

## Key findings

- Magnetisation acts as an order parameter for the chiral transition.
- A universal relation links $(B)$ and magnetisation.
- Results agree with previous semi-analytic approximations at low temperatures.

## 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 [JHEP 1103 (2011) 033], based on a semi-analytic approximation.