AdS/BCFT correspondence and Horndeski gravity in the presence of gauge fields: holographic paramagnetism/ferromagnetism phase transition

TL;DR

This paper develops a holographic model using Horndeski gravity to study phase transitions between paramagnetism and ferromagnetism in a (2+1)-dimensional system, revealing effects of magnetic fields and gravity modifications on magnetic properties.

Contribution

It introduces a dual gravity model incorporating Horndeski gravity terms to analyze holographic paramagnetism-ferromagnetism transitions with magnetic fields and charge density.

Findings

Increasing Horndeski parameter lowers critical temperature.

Magnetic field supports localized condensate with quantum Hall behavior.

Spontaneous magnetization occurs at low temperatures.

Abstract

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 we increase the Horndeski gravity parameter, that is represented by $\gamma$. Furthermore, such condensate shows quantum Hall-type behavior. This radius is also inversely related to the total action coefficients of our model. It was 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. We also found that at low temperatures, spontaneous magnetization and ferromagnetic phase transition.