Lifshitz scaling effects on the holographic paramagnetic-ferromagnetic phase transition

TL;DR

This paper investigates how Lifshitz dynamical exponent $z$ influences holographic paramagnetic-ferromagnetic phase transitions, revealing that critical temperature decreases with increasing $z$, and confirming universal critical exponents and Curie-Weiss law behavior.

Contribution

It introduces a study of Lifshitz scaling effects on holographic magnetic phase transitions using Power-Maxwell electrodynamics and a massive 2-form field, with numerical analysis in the probe limit.

Findings

Critical temperature decreases with increasing $z$ and power parameter $q$.

Spontaneous magnetization occurs at low temperatures without external magnetic field.

Critical exponent $eta=1/2$ is universal across parameters.

Abstract

We disclose the effects of Lifshitz dynamical exponent $z$ on the properties of holographic paramagnetic-ferromagnetic phase transition in the background of Lifshitz spacetime. To preserve the conformal invariance in higher dimensions, we consider the Power-Maxwell (PM) electrodynamics as our gauge field. We introduce a massive $2$-form coupled to the PM field and perform the numerical shooting method in the probe limit by assuming the PM and the $2$-form fields do not back-react on the background geometry. The obtained results indicate that the critical temperature decreases with increasing the strength of the power parameter $q$ and dynamical exponent $z$. Besides, the formation of the magnetic moment in the black hole background is harder in the absence of an external magnetic field. At low temperatures, and in the absence of an external magnetic field, our result show the spontaneous magnetization and the ferromagnetic phase transition. We find that the critical exponent takes the universal value $\beta= 1/2$ regardless of the parameters $q, z, d$, which is in agreement with the mean field theory. In the presence of an external magnetic field, the magnetic susceptibility satisfies the Curie-Weiss law.