Holographic paramagnetic-ferromagnetic phase transition of Power-Maxwell-Gauss-Bonnet black holes

Based on the shooting method, we numerically investigate the properties of holographic paramagnetism-ferromagnetism phase transition in the presence of higher order Gauss-Bonnet (\emph{GB}) correction terms on the gravity side. On the matter field side, however, we consider the effects of the Power-Maxwell (\emph{PM}) nonlinear electrodynamics on the phase transition of this system. For this purpose, we introduce a massive $2-$form coupled to \emph{PM} field, and neglect the effects of $2-$form fields and gauge field on the background geometry. We observe that increasing the strength of both the power parameter $q$ and \emph{GB} coupling constant $\alpha$ decrease the critical temperature of the holographic model, and lead to the harder formation of magnetic moment in the black hole background. Interestingly, we find out that at low temperatures, the spontaneous magnetization and ferromagnetic phase transition happen in the absence of external magnetic field. In this case, the critical exponent for magnetic moment has the mean field value, $1/2$, regardless of the values of $q$ and $\alpha$. In the presence of external magnetic field, however, the magnetic susceptibility satisfies the Curie-Weiss law.