In the Weiss molecular-field approximation, the
S=1 Ising-model ferromagnet possessing additional single-ion-type uniaxial anisotropy is known to exhibit (depending upon the ratio of anisotropy and interaction constants) both first-order (discontinuous) and second-order (continuous) magnetic phase transitions which join at a tricritical point. We further investigate the above model system in the spin-pair approximation using the cluster-variation method. Within this improved approximation, results are found for the temperature and anisotropy dependences of the thermal-average quantities
〈Si〉,
〈Si2〉, $〈{S}_{i}{S}_{{i}^{\ensuremath{'}}}〉$, $〈{S}_{i}S_{{i}^{\ensuremath{'}}}^{}{}_{}{}^{2}〉$, $〈S_{i}^{}{}_{}{}^{2}S_{{i}^{\ensuremath{'}}}^{}{}_{}{}^{2}〉$ (
i, ${i}^{\ensuremath{'}}$ are nearest-neighbor lattice sites), a better estimate for the location of the tricritical point is achieved, and the specific heat and initial paramagnetic susceptibility are calculated. To illustrate these results, the simple cubic lattice is used as an example of application.