Holographic paramagnetism–ferromagnetism phase transition with the nonlinear electrodynamics

Abstract

In the probe limit, we investigate the nonlinear electrodynamical effects of the both exponential form and the logarithmic form on the holographic paramagnetism-ferromagnetism phase transition in the background of a Schwarzschild-AdS black hole spacetime. Moreover, by comparing the exponential form of nonlinear electrodynamics with the logarithmic form of nonlinear electrodynamics and the Born-Infeld nonlinear electrodynamics which has been presented in Ref.[55], we find that the higher nonlinear electrodynamics correction makes the critical temperature smaller and the magnetic moment harder form in the case without external field. Furthermore, the increase of nonlinear parameter b will result in extending the period of the external magnetic field. Especially, the effect of the exponential form of nonlinear electrodynamics on the periodicity of hysteresis loop is more noticeable.

Holographic paramagnetic-ferromagnetic phase transition with Power-Maxwell electrodynamics

“…It means that the magnetic moment is harder to be formed. This behavior have been reported previously in [25] too. Fig.…”

“…As it can be found from this Figure, the magnetic moment decreases with increasing the power parameter α. It means that the magnetic moment is harder to be formed which is in a good agreement with similar works [25,26]. This behavior has been seen for the holographic superconductor in the Schwarzschild-AdS black hole, where the three types of nonlinear electrodynamics make scalar condensation harder to be formed [35].…”

“…In Table II, our numerical results for critical temperature with different values of power parameter α and for two cases of dimensions(d = 4, 5) are presented. In the Maxwell limit (α → 1), our numerical results reproduce the ones of [25] for d = 4. We see from Table II that the critical temperature T c increases by decreasing the power parameter for fixed dimension.…”

“…In other words, the holographic paramagnetic-ferromagnetic phase transition exists by considering the Power-Maxwell electrodynamics similar to the cases of Born-Infeld-like nonlinear electrodynamic discussed in Ref. [25]. As it can be found from this Figure, the magnetic moment decreases with increasing the power parameter α.…”

“…However, it is interesting to investigate the effects of nonlinear electrodynamics on the properties of the holographic paramagnetic-ferromagnetic phase transition. Considering three types of nonlinear electrodynamics, namely, Born-Infeld, logarithmic and exponential nonlinear electrodynamics, and using the numerical methods, it has been observed that in the Schwarzschild AdS black hole background, the higher nonlinear electrodynamics corrections make the magnetic moment harder to form in the absence of external magnetic field [25,26]. Although, the properties of holographic superconductor with conformally invariant Power-Maxwell electrodynamics have been studied in [27][28][29][30][31], the properties of holographic paramagnetic-ferromagnetic phase transition coupled to the Power-Maxwell field have not been explored yet.…”