Lifshitz scaling effects on the holographic paramagnetic-ferromagnetic phase transition

We disclose the effects of Lifshitz dynamical exponent $z$ on the properties of holographic paramagnetic-ferromagnetic phase transition in the background of 4D and 5D Lifshitz spacetime. To preserve the conformally invariance in higher dimensions, we consider the Power-Maxwell (PM) electrodynamics as our gauge field. We introduce a massive $2$-form coupled to the PM field and perform the numerical shooting method in the probe limit by assuming the PM and the $2$-form fields do not back react on the background geometry. The results indicate that the critical temperature decreases with increasing the strength of the power parameter $q$ and dynamical exponent $z$. Besides, the formation of magnetic moment in the black hole background is harder in the absence of an external magnetic field. At low temperatures, when there is no external magnetic field, our result show the spontaneous magnetization and the ferromagnetic phase transition. We find that the critical exponent has its universal value of $\beta= 1/2$ regardless of the parameters $q, z$ as well as dimension d, which is in agreement with the result of the mean field theory. In the presence of external magnetic field, the magnetic susceptibility satisfies the Cure-Weiss law.