# Holographic paramagnetic-ferromagnetic phase transition with Power-Maxwell electrodynamics

## TL;DR

This paper investigates how Power-Maxwell nonlinear electrodynamics influences holographic paramagnetic-ferromagnetic phase transitions in Schwarzschild AdS black holes, revealing effects on magnetic moment formation, critical temperature, and susceptibility behavior.

## Contribution

It introduces a massive 2-form coupled to Power-Maxwell fields to study nonlinear effects on magnetic phase transitions in holography, using numerical methods in the probe limit.

## Key findings

- Increasing power parameter makes magnetic moment formation harder.
- Critical temperature decreases with higher power parameter.
- Magnetic susceptibility follows Curie-Weiss law in external magnetic fields.

## Abstract

We explore the effects of Power-Maxwell nonlinear electrodynamics on the properties of holographic s-wave paramagnetic-ferromagnetic phase transition in the background of Schwarzchild Anti-de Sitter (AdS) black hole. For this purpose, we introduce a massive 2-form coupled to the Power-Maxwell field. We perform the numerical shooting method in the probe limit by assuming the Power-Maxwell and the 2-form fields do not back react on the background geometry. We observe that increasing the strength of the power parameter causes the formation of magnetic moment in the black hole background harder and critical temperature lower. In the absence of external magnetic field and at the low temperatures, the spontaneous magnetization and the ferromagnetic phase transition happen. In this case, the critical exponent for magnetic moment is always 1/2 which is in agreement with the result from the mean field theory. In the presence of external magnetic field, the magnetic susceptibility satisfies the Cure-Weiss law.