  The internal energies, including transverse and longitudinal parts, of
quantum Heisenberg systems for arbitrary spin S are investigated by the
double-time Green's function method. The expressions for ferromagnetic (FM) and
antiferromagnetic (AFM) systems are derived when one component of magnetization
is considered with the higher order longitudinal correlation functions being
carefully treated. An unexpected result is that around the order and disorder
transition points the neighboring spins in a FM (AFM) system are more likely
longitudinally antiparallel (parallel) than parallel (antiparallel) to each
other for S<=3/2 in spite of the FM (AFM) exchange between the spins. This is
attributed to the strong quantum fluctuation of the systems with small S
values. We also present the expressions of the internal energies of FM systems
when the three-component of magnetizations are considered.
