  The present study regards the zeroth order mean field approximation of a
dipole-type interaction model, which is analytically solved in the canonical
and microcanonical ensembles. After writing the canonical partition function,
the free and internal energies, magnetization and the specific heat are derived
and graphically represented. A crucial derivation is the calculation of the
free energy, which is variationally evaluated, and it is shown that the exact
result coincides with the approximate trend when $N$ tends to infinity. In the
microcanonical ensemble, the entropy as other thermodynamic properties are
calculated. We notice that both schemes coincide in equilibrium.
