Quasicollective spin waves in the paramagnetic region of an anisotropic Heisenberg ferromagnet

A second-order theory is constructed for an anisotropic Heisenberg ferromagnet of the easy axis type. The theory is based on the method of the equations of motion for the Green's functions. The contribution of the fluctuations of the magnon density operator is taken into account partly in the linearization. It is shown that in the region of sufficiently large momenta the poles of the single-particle Green's function have the ordinary spin-wave dispersion law, and the renormalization is determined by the correlation functions of the short-range order. The reciprocal correlation radius is estimated, and this agrees with phenomenological theory.