Lifshitz scaling effects on the holographic model for paramagnetism-antiferromagnetism phase transition

Abstract

In this work, we construct a holographic antiferromagnetism model by introducing two real antisymmetric tensor fields coupling to the background gauge field strength and interacting with each other in the four-dimensional Lifshitz black hole, and investigate the effects of Lifshitz dynamical exponent z on the paramagnetism-antiferromagnetism phase transition in detail. Using the numerical shooting method, we find that there is still a phase transition in asymptotically Lifshitz space-time in the probe limit. In the absence of an external magnetic field and in low temperature, the magnetic moments condense spontaneously in antiparallel manner with the same magnitude. But the critical temperature and the staggered magnetization decrease with increasing z, which makes paramagnetism-antiferromagnetism phase transition harder to happen. In the presence of the weak external magnetic field, the magnetic susceptibility has a peak at the critical temperature and increasing values of z makes the peak higher. In the case of the strong external magnetic field, there exists a critical magnetic field Bc in the antiferromagnetic phase. When the magnetic field reaches Bc, the system turns into the paramagnetic phase. Besides, the increasing of z results in increasing of Bc.