Numerical studies on holographic paramagnetic-ferromagnetic phase transition in Gauss-Bonnet gravity

Based on the shooting method, we numerically investigate the properties of holographic paramagnetism-ferromagnetism phase transition in the presence of higher-order Gauss-Bonnet (GB) correction terms on the gravity side. On the matter field side, however, we consider the effects of Power-Maxwell (PM) nonlinear electrodynamics on the phase transition of this system. For this purpose, we introduce a massive 2-form coupled to 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 GB coupling constant a decreases the critical temperature of holographic model, and leads 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 a. In the presence of external magnetic field, however, the magnetic susceptibility satisfies the Curie-Weiss law.