The second order phase transitions of the spin-1 Ising model on pure Husimi lattices with elementary triangles: Exact results

• Exact analysis of spin-1 Ising model on “triangular” Husimi lattices is performed.
• Equation for exact determination of the critical points of the spin-1 Ising model is found.
• Exact expression for the spontaneous magnetization on the lattice with z=4z=4 is found.

We investigate the second order phase transitions of the ferromagnetic spin-1 Ising model on pure Husimi lattices built up from elementary triangles with arbitrary values of the coordination number. An explicit equation is derived for exact determination of the critical temperatures of the second order phase transitions simultaneously on all such lattices. It is shown that for arbitrary given value of the coordination number this equation is equivalent to the corresponding polynomial equation. In addition, an exact explicit expression is found for the spontaneous magnetization on the simplest lattice with coordination number z=4z=4.