Abstract: Intrinsic energy of two-dimensional square lattice single-ion anisotropic Heisenberg ferromagnets,antiferromagnets,and ferromagnetic single-walled nanotubes are calculated with many-body Green's function method in quantum statistical theory.Calculated results of ferromagnets and antiferromagnets are compared.Between zero temperature and phase transition point,including zero temperature,anti-ferromagnetic energy is always lower than that of ferromagnetic energy.Calculation method of intrinsic energy in this paper is applicable not only to ferromagnetic system,but also suitable for antiferromagnetic system and ferrimagnetic system,as well as ferromagnetic single-walled nanotubes.Intrinsic energies are greatly lower than classical energies, which shows that transverse correlation effect is important.

Key words: Heisenberg model, two-dimensional systems, magnetic nanotubes, intrinsic energy, many-body Green's function method