Аннотация:The approximation of nearest neighbor interaction (NNI) is widely used in short-time spin dynamics with dipole-dipole interactions (DDI) when the intensity of spin-spin interaction is 1/r^3, where r is a distance between those spins. However, NNI can not approximate the long time evolution in such systems. We consider the system with the intensity of the spin-spin interaction 1/r^\alpha, \alpha>=3 , and find the low boundary \alpha_c of applicability of the NNI to the evolution of an arbitrary one-excitation initial quantum state in the homogeneous spin chain governed by the XX-Hamiltonian. We obtain the logarithmic dependence of \alpha_c on the chain length.