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

A solvable problem in statistical mechanics: the dipole-type Hamiltonian mean field model