Green's function theory of linear magnetic chains with anisotropic coupling

The one-dimensional spin-1/2 ferromagnetic and antiferromagnetic chains with anisotropic coupling are studied within the Green's function theory in both planar and uniaxial regimes. The spin Green's functions are decoupled at a stage one-step further than the Tyablikov's decoupling under the constraint [S-z] = 0. The behaviors of the correlation functions are studied in the entire temperature regime. The thermodynamic properties are also discussed, and the result is consistent with the numerical simulation.