AdS/BCFT Correspondence and Horndeski Gravity in the Presence of Gauge Fields: Holographic Paramagnetism/Ferromagnetism Phase Transition

This paper presents a dual gravity model for a (2+1)-dimensional system with a limit on finite charge density and temperature, which will be used to study the properties of the holographic phase transition to paramagnetism-ferromagnetism in the presence of Horndeski gravity terms. In our model, the non-zero charge density is supported by a magnetic field. As a result, the radius $\rho /B$ indicates a localized condensate, as the Horndeski gravity parameter is increased, that is represented by γ. Furthermore, such condensate shows quantum Hall-type behavior. This radius is also inversely related to the total action coefficients of our model. It is observed that increasing the Horndeski parameter decreases the critical temperature of the holographic model and leads to the harder formation of the magnetic moment at the bottom of the black hole. However, when removing the magnetic field, the ferromagnetic material presents a disorder of its magnetic moments, which is observed through the entropy of the system. The authors also found that at low temperatures, spontaneous magnetization and ferromagnetic phase transition.