The critical behavior of the mixed spin-1 and spin-2 Ising ferromagnetic system on the Bethe lattice

Abstract

The phase diagrams of the mixed spin-1 and spin-2 Blume–Capel Ising ferromagnetic system ( J > 0 ) with two crystal-field interactions, D A for spin-1 and D B for spin-2, is studied on the Bethe lattice by using the exact recursion equations. The exact expressions of the order-parameters for the sublattices with spin-1 and spin-2, and the Curie temperature and the free energy of the system are obtained in terms of the recursion relations. The phase diagrams on the ( kT c / J , D A / J ) and ( kT c / J , D B / J ) planes are studied for selected values of D B / J and D A / J , respectively, for the coordination numbers q = 3 , 4 , and 6. Besides the second-order phase transition lines, the lines of the first-order phase transitions terminating either at a tricritical point or at an isolated critical point are found.