Abstract
In this paper, we investigate in some detail the holographic ferromagnetic phase transition in an AdS${_4}$ black brane background by introducing a massive 2-form field coupled to the Maxwell field strength in the bulk. In the two probe limits, one is to neglect the back reaction of the 2-form field to the background geometry and to the Maxwell field, and the other to neglect the back reaction of both the Maxwell field and the 2-form field, we find that the spontaneous magnetization and the ferromagnetic phase transition always happen when the temperature gets low enough with similar critical behavior. We calculate the DC resistivity in a semi-analytical method in the second probe limit and find it behaves as the colossal magnetic resistance effect in some materials. In the case with the first probe limit, we obtain the off-shell free energy of the holographic model near the critical temperature and compare with the Ising-like model. We also study the back reaction effect and find that the phase transition is always second order. In addition, we find an analytical Reissner-Norstr\"om-like black brane solution in the Einstein-Maxwell-2-form field theory with a negative cosmological constant.
Highlights
Most of attentions about the duality application to condensed matter physics have been focused on the electronic properties of materials
In this paper we investigate in some detail the holographic ferromagnetic phase transition in an AdS4 black brane background by introducing a massive 2-form field coupled to the Maxwell field strength in the bulk
One is to neglect the back reaction of the 2-form field to the background geometry and to the Maxwell field, and the other to neglect the back reaction of both the Maxwell field and the 2-form field, we find that the spontaneous magnetization and the ferromagnetic phase transition always happen when the temperature gets low enough with similar critical behavior
Summary
V (Mμν) is a nonlinear potential of the 2-form field. It describes the self-interaction of the polarization tensor, which should be expanded as the even power of Mμν. In this model, we take the following form,. In the AdS/CFT correspondence, a hairy black hole with appropriate boundary conditions can be explained as a condensed phase of the dual field theory, while a black hole without hair is dual to a normal phase. When Mμν vanishes, the model admits the AdS Reissner-Nordstrom (RN) black brane solution, which corresponds to the normal phase in the dual field theory. When we lower the temperature, the system exhibits an instability which triggers to break time reversal symmetry spontaneously as well as spatial rotation symmetry since the condensate will pick out one direction as special (if spatial dimension is more than 2) and the paramagnetism/ferromagnetism phase transition happens
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