We assume that the free energy of the system is a functional of order parameter. In the vicinity of second order transition, the free energy density can be expanded as a power series of order parameter as well as its correlation term. Following the pro-cedure given here, for both local and non-local, the order parameter representing equilibrium configuration can be found from the vanishment of the first variation of free energy. In order to find out the solution, it is necessary to carry out Fourier transform for order parameter, and this is identical to expand the order parameter in terms of the base functions of symmetric group of the system. In this way, we analyse the change of symmetry in second order transition.By making use the necessary and sufficient condition (or sufficient condition) for extrema in the variational procedure, the condition of stability for states in second order transition is discussed. Because the correlation term has not been neglected in the procedure of finding extrema, so that the restrictions condition of Lifshitz on sym-metry changing does not come into being. It should be pointed out that, in Lifshitz approach the correlation term is neglected in obtaining the minimum of free energy functional, whereas it is included in discussing the problem of stability. Therefore, Lifshitz's approach is inconsistent in itself. Furthermore, there exists certain kinds of system (such as one component axial vector system), in which the correlation term that leads to the Lifshitz condition cannot be constructed from order parameter. Nevertheless, Lifshitz and others also put restrictions on such system. This is obviously unreasonable. By making use the general theoretical approach described above, we explain the experimental results of phase transition in heavy lanthanide metals at Neel point. It serves as an example to show that there are second order phase transition phenomena for which Lifshitz's approach fails to explain.