Holographic model for ferromagnetic phase transition in the Lifshitz black hole with the nonlinear electrodynamics

We numerically investigate the holographic paramagnetism-ferromagnetism phase transition in the 4-dimensional Lifshitz spacetime in the presence of three kinds of typical Born-Infeld-likenonlinear electrodynamics. Concretely, in the probe limit, we thoroughly discuss the effects of the nonlinear parameter band the dynamical exponent zon the critical temperature, magnetic moment and hysteresis loop. The resultsshow that the exponential form of nonlinear electrodynamics correction makes the critical temperature smaller and the magnetic moment harder to formwith the absent external field for a constant nonlinear parameter bcomparingit with the logarithmic form of nonlinear electrodynamics and the Born-Infeld nonlinear electrodynamics, especially for the case of larger dynamical exponentz. Moreover, the increase of nonlinear parameterb(forthe fixedz) or dynamical exponentz(forthe fixedb) will result in extending the period of the external magnetic field. Particularly, the effect of the exponential form of nonlinear electrodynamics on the periodicity of hysteresis loop is more noteworthy. (C) 2017 The Authors. Published by Elsevier B.V.