One-particle green s function in the anisotropic Heisenberg model

The matrix Green function is studied which is constructed in terms of the Pauli operators and describes the transversal component of the dynamic susceptibility tensor of the anisotropic Heisenberg ferromagnet with spin 1/2 in the transversal and longitudinal external magnetic field. Renormalised magnon spectrum is obtained in the generalised Hartree–Fock approximation (with the damping not taken into account) and phase boundary on the plane “magnetic field – temperature” is evaluated. It is shown that the contribution of the integral term must be taken into account for the fulfillment of the symmetry conditions and the Goldstone–Bogoliubov theorem in the case of the “easy plane” model.