Phase diagrams and the thermal variations of the order‐parameters in the mixed spin‐1 and spin‐$3 \over 2$ ising model on the Bethe lattice

Abstract

AbstractThe mixed spin‐1 and spin‐$3 \over 2$ Blume‐Capel Ising ferromagnetic system (J > 0) with two crystal‐field interactions, DA for spin‐1 and DB for spin‐$3 \over 2$, is studied on the Bethe lattice using the exact recursion equations for the central‐spin with spin‐$3 \over 2$. The exact expressions for the order‐parameters, the Curie temperature and the free energy are obtained in terms of the recursion relations. The phase diagrams on the $\bigg ({{kT_c}\over{J}}, \,{{D_A}\over{J}}\bigg )$ and $\bigg ({{kT_c}\over{J}}, \,{{D_B}\over{J}}\bigg )$ planes are studied for selected values of DB/J and DA/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. The thermal variations of the order‐parameters are studied with two formulations, both obtained on the Bethe lattice for the mixed spin‐1 and spin‐$3 \over 2$ Ising system using the exact recursion relations, but one with the central‐spin with spin‐1 and the other is for the central‐spin with spin‐$3 \over 2$ for q = 3, thus, it is shown that the choice of the central‐spin on the Bethe lattice has no effect on the phase diagrams.