Lifshitz scaling effects on holographic paramagnetism/ferromagneism phase transition

TL;DR

This paper explores how Lifshitz scaling influences holographic paramagnetism-ferromagnetism phase transitions, revealing that the dynamical exponent $z$ affects magnetic properties and phase transition behavior in higher-dimensional black hole models.

Contribution

It provides a detailed analysis of Lifshitz scaling effects on magnetic phase transitions using numerical and semi-analytical methods in holographic models, highlighting the role of the dynamical exponent $z$.

Findings

Lifshitz exponent $z$ affects magnetic moment and hysteresis loops quantitatively.

Spontaneous magnetization occurs at low temperatures with a critical exponent of 1/2.

Increasing $z$ enhances phase transition and DC resistivity, resembling colossal magnetic resistance.

Abstract

In the probe limit, we investigate holographic paramagnetism-ferromagnetism phase transition in the four-dimensional (4D) and five-dimensional(5D) Lifshitz black holes by means of numerical and semi-analytical methods, which is realized by introducing a massive 2-form field coupled to the Maxwell field. We find that the Lifshitz dynamical exponent $z$ contributes evidently to magnetic moment and hysteresis loop of single magnetic domain quantitatively not qualitatively. Concretely, in the case without external magnetic field, the spontaneous magnetization and ferromagnetic phase transition happen when the temperature gets low enough, and the critical exponent for the magnetic moment is always $1/2$, which is in agreement with the result from mean field theory. And the increasing $z$ enhances the phase transition and increases the DC resistivity which behaves as the colossal magnetic resistance effect in some materials. Furthermore, in the presence of the external magnetic field, the magnetic susceptibility satisfies the Cure-Weiss law with a general $z$. But the increase of $z$ will result in shortening the period of the external magnetic field.