Influence of lattice dimensionality and quantum fluctuations on the kinematic interaction of spin waves

Effect of the lattice dimensionality and quantum fluctuations on the strength of kinematical interaction of spin waves is studied. It is shown that in the quasi-low-dimensional spin systems the effects of finite-dimensionality of the spin space are exponentially small even if the density of spin waves is large (the mean number of excitations per site is equal to the value of the spin in this site). In systems with non-collinear spin structure quantum fluctuations of the vacuum reduce the strength of kinematical interaction.