Abstract
The effective-field model of a spin-1 Ising system with both dipolar and quadrupolar interactions is studied. From the generalized Suzuki identity the exact expressions for the dipolar and the quadrupolar ordering parameters are found in the form of ensemble averages. Two different operators are introduced to write the above expressions in the form of exponentials, which are then simplified. The transition temperatures for linear, honeycomb, and simple cubic lattices are computed and compared with the results of previous theories.