Research On The Application Of Gravitational Holographic Dual Theory In Ferromagnetic Phase Transition

The unusual magnetic materials are significants in both society and science.However,because of the strongly correlated effects,it is difficult to understand the novel properties of such materials from theoretical aspects.Holographic duality theory offers a new tool to investigate the strongly correlated quantum system from weakly coupling gravity.This dissertation aims to introduce our studies on strongly correlated system controlled by magnetism from holographic duality.At first,we construct a holographic paramagnetism-ferromagnetism phase transition in four-dimensional and five-dimensional Lifshitz black holes by means of numerical and semianalytical methods in the probe limit,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 the magnetic moment and hysteresis loop of single magnetic domain quantitatively,not qualitatively.When the external magnetic field is zero and the temperature gets low enough,the spontaneous magnetization and ferromagnetic phase transition happen,and near the critical temperature Tc,the critical exponent for the magnetic moment is always 1/2 that is in agreement with the result from the mean field theory.At the same time,the increasing of the Lifshitz scaling parameter z will enhance the phase transition and increase the dc resistivity,which behaves as the colossal magnetic resistance effect in some materials.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.Secondly,we get rid of the conventional Maxwell electrodynamic theory,and study the effect of nonlinear electrodynamic theories on the magnetic sys-tem.It turned out that the higher derivative corrections of the gauge field carry more plentiful information than the usual Maxwell electrodynamics.One of the most popular nonlinear electromagnetic theories is Born-Infeld electrodynamic-s.We investigate the effects of the Born-Infeld electrodynamics on the holo-graphic paramagnetism-ferromagnetism phase transition in the background of a 4-dimensional Schwarzschild-AdS black hole.We find that the nonlinear param-eter b hinder the phase transition and make the magnetic moment harder to form.Finally,we investigate the holographic paramagnetism-ferromagnetism phase transition in the 4-dimensional Schwarzschild black hole and Lifshitz black hole,respectively,by coupling 2-form field to the two kinds of nonlinear electrody-namics(exponential form of nonlinear electrodynamics and logarithmic form of nonlinear electrodynamics)and comparing with the Born-Infeld electrodynam-ic.In the case without external magnetic field,by comparing the three kinds of typical Born-Infeld-like nonlinear electrodynamics,we find that the three kinds of higher nonlinear corrections make the critical temperature Tc and magnetic moment N decrease,i.e.,hinder the phase transition.Moreover,no matter which spacetime we choose,near the critical temperature Tc,the exponential form of nonlinear electrodynamics makes the critical temperature smaller and the mag-netic moment harder to form,especially for the case of larger dynamical exponent z.Similarly,the effect of the exponential form of nonlinear electrodynamics on the periodicity of hysteresis loop is more noteworthy.