Symmetry of a magnet and behavior of quasiparticle spectra at low momenta

A special representation for the spin operators is used to show that the spectrum of a magnet with an arbitrary number of sublattices for which the symmetry of the ground state is lower than the symmetry of the Hamiltonian contains at least one symmetry mode whose energy and damping tend to zero when the wave vector tends to zero (analog of Goldstone's theorem). This assertion remains true in any perturbation order.