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

The present study documents a type of mean field approximation inspired by the dipole interaction model, which is analytically solved in the canonical and microcanonical ensembles. The current calculations were derived from the Hamiltonian mean field model developments. After describing the canonical partition function, the free and internal energies, magnetization, and specific heat are derived and graphically depicted. In the microcanonical ensemble, the entropy is calculated as well as other thermodynamic properties. The system shows a second-order phase transition emphasizing that both methods coincide, which is only valid only in equilibrium. In addition, the current model represents a nonsymmetric Hamiltonian mean field model that shows a phase transition.