The phase diagrams of the mixed-spin ternary-alloy consisting of half-integer spins: Standard-random approach

Highlights: • The ternary-alloy in the form AB_pC_1-p is investigated on the Bethe lattice. • The standard-random approach is used instead of the site-dependent random one. • Half-integer spins are considered to form the ternary alloy: spin- ½, spin- 3/2 and spin- 5/2. • The phase diagrams are obtained on the (p; kTc/JAB) and (R; kTc/JAB) planes. • The critical value of R, i.e. Rc = 0.653 is independent of z. - Abstract: The ternary-alloy in the form ${AB}_p{C}_{1-p}$ is investigated on the Bethe lattice with the odd numbered shells containing only $A$ atoms (spin-$\frac{1}{2}$), while the even shells randomly containing either $B$ (spin-$\frac{3}{2}$) or $C$ (spin-$\frac{5}{2}$) atoms with different concentrations $p$ and $1-p$, respectively. The phase diagrams are calculated on the $\left(p,{kT}_c/J_{AB}\right)$ and $\left(R=\left|J_{AC}\right|/J_{AB},{kT}_c/J_{AB}\right)$ planes for given values of $R$ and $p$, respectively, with the coordination numbers $z=3,4,5$ and 6 by studying the thermal variations of the order-parameters. It is found that there exist a critical value of $R$, i.e. $R_c\cong 0.653$, which is independent of $z$. In addition, the critical temperatures increase as $z$ increases. The present work is an extension of the previous work [1] and it only differs from it by the implementation technique of randomness into the model. The obtained phase diagrams are in agreement with the site-dependent random case [1] except at low temperatures. On the other hand, there is an overall agreement with the literature.