The Application Of Gauge/Gravity Duality In Holographic Ferromagnetism And Antiferromagnetism Phase Transition

The special magnetic materials play an important role in the development of technology.While due to the strong correlation effect between electrons in these magnetic materials,it will be difficult for us to theoretically explain some of the properties that materials exhibit.However there is a new approach to investigate the strongly correlated quantum system,which is the gauge/gravity duality.So this paper will introduce the applications of the dual in strongly correlated ferromagnetism and anti-ferromagnetism systems.The ferromagnetic model has been successfully constructed in the framework of classical Maxwell electrodynamics.With the in-deep exploration of the ferromagnetic model in nonlinear electrodynamics,it is found that the nonlinear electrodynamics carries more abundant information than the classical Maxwell electrodynamics.Hence,in the probe limit and in the background of a Schwarzschild-Ad S black hole with the Power-Maxwell field,we will research the holographic paramagnetism-ferromagnetism phase transition and related properties.When the external magnetic field is zero,the values of the critical temperature and the magnetic moment with the different power parameter q are carried out.It can be seen that the increasing of q reduces the critical temperature and the spontaneous magnetic moment,which makes it harder for the phase transition to be formed.In the presence of an external magnetic field,we get the values of the magnetic susceptibility density with the different q,and the magnetic susceptibility density satisfies the Cure-Weiss law.When the external magnetic field changes periodically,the hysteresis loop in the single magnetic domain appears,and the increasing of q lengthens the period of external magnetic field.Except for the holographic ferromagnetic model,we introduce two real antisymmetric tensor fields coupling to the background gauge field strength and interacting with each other under the background of the four-dimensional Lifshitz black hole,which makes a holographic paramagnetism-antiferromagnetism phase to realize.And then the effects of Lifshitz dynamical exponent z on the phase transition are discussed detailedly.In the probe limit and using the numerical shooting method,we find that there is still a phase transition in asymptotically Lifshitz space-time.When there is no external magnetic field and in low temperature,the magnetic moment has the behavior of spontaneous condensation.But the critical temperature and the staggered magnetization decrease with increasing z,which makes the phase transition harder to happen.When the external magnetic field is weaker,the magnetic susceptibility density has a maximum at the critical temperature and increasing values of z makes the peak higher.When the external magnetic field is stronger,there will be a critical magnetic field.When the external magnetic field reaches critical magnetic field,the system turns into the paramagnetic phase,and the increasing of z results in increasing of critical magnetic field.