Landau theory of dynamic phase transitions and systematic perturbation expansion method for getting phase diagrams

We propose a systematic perturbation expansion method for getting phase diagrams on dynamical symmetry breaking which is caused by varying the amplitude h or frequency Ω of the periodic external force h cos(Ωt) in systems under the Landau type potentials. The method is based on the Fourier expansion and the Floquet theorem. We formulate the method by utilizing an introductory example, bistable system driven by the periodic external force. An order estimation criterion based on the magnitude of the Fourier coefficient for the fundamental frequency Ω plays an essential role in order to construct the systematic expansion method. According to the criterion, analytical expressions for the transition point and weak nonlinear expansions (Landau type expansions) near the transition point are derived in desired orders of approximation. We also show two applications of the method: the dynamical symmetry breaking in the XY-spin system with uniaxial anisotropy and tristable system at the presence of the forcing. The method predicts all behaviors of phase diagrams on those. The latter example may be the first legitimate treatment of subcritical pitchfork bifurcation in the frameworks of the dynamic phase transition.