The dynamical longitudinal correlation function of the Heisenberg model at low temperatures

The dynamical longitudinal correlation function of the low-temperature Heisenberg ferromagnet is studied in the collisionless regime. Taking into account the kinematical effects, a kinetic equation is derived in this regime describing the system only in terms of interacting spin-waves. The corresponding effective potential is shown to be too weak to support the existence of a high-frequency collective mode (zero magnon).