Development of the Green function diagrammatic technique for local spins

We show using as an example of the singlet-singlet (the transverse Ising model) model how the renormalization of local propagators and population factors may be achieved in the frame of the loop expansion of the self-energy. By this the Green function diagrammatic technique for interacting local spins in the presence of the crystalline field becomes free from shortcomings induced by the practice in which only the interaction undergoes the renormalization. The low order renormalization of the propagators leads to the calculated high-temperature (T→∞) frequency shift while the population renormalization reduces the ferromagnetic T_c.