  An Ornstein-Zernike approximation for the two-body correlation function
embodying thermodynamic consistency is applied to a system of classical
Heisenberg spins on a three-dimensional lattice. The consistency condition
determined in a previous work is supplemented by introducing a simplified
expression for the mean-square fluctuations of the spin on each lattice site.
The thermodynamics and the correlations obtained by this closure are then
compared with approximants based on extrapolation of series expansions and with
Monte Carlo simulations. The comparison reveals that many properties of the
model, including the critical temperature, are very well reproduced by this
simple version of the theory, but that it shows substantial quantitative error
in the critical region, both above the critical temperature and with respect to
its rendering of the spontaneous magnetization curve. A less simple but
conceptually more satisfactory version of the SCOZA is then developed, but not
solved, in which the effects of transverse correlations on the longitudinal
susceptibility is included, yielding a more complete and accurate description
of the spin-wave properties of the model.
