Tyablikov approximation in the theory of low-dimensional quantum Heisenberg ferromagnets and antiferromagnets

The method of double-time-temperature spin Green functions is used to develop the theory of low-dimensional quantum Heisenberg ferromagnets and antiferromagnets with arbitrary spin. In the Tyablikov approximation, the correlation functions, the susceptibility of ferromagnets, and the staggered susceptibility of antiferromagnets as well as the magnetic-field dependence of the magnetization for ferromagnets are found. The formulas derived describe ferromagnets and antiferromagnets at arbitrary temperatures and interpolate the regions of low-temperature and high-temperature behavior. It is paramagnetic temperature that separates the regions of different analytical behavior of the system parameters.