The second order phase transitions of the Ising model on tetrahedron recursive lattices: Exact results

We investigate the ferromagnetic spin-1/2 Ising model on the so-called tetrahedron recursive lattices with arbitrary coordination numbers. First, the concept of the tetrahedron recursive lattice is introduced which can be considered as the simplest but effective approximation of real tetrahedron lattices which takes into account their basic geometric properties. An explicit analytic formula for exact determining of the values of the critical temperatures of the second order phase transitions simultaneously on all tetrahedron recursive lattices is derived. In addition, an exact explicit expression for the spontaneous magnetization on the simplest tetrahedron recursive lattice with the coordination number z=6 is also found.