The quaternary alloy on the Bethe lattice

The quaternary alloy (QA) is simulated on the Bethe lattice (BL) in the form of ABpCqDr and its phase diagrams are calculated by using the exact recursion relations (ERR) for the coordination number z = 3. The QA is designed on the BL by placing A atoms (spin-1/2) on the odd shells and randomly placing B (spin-3/2), C (spin-5/2) or D (spin-1) atoms with probabilities p, q and r, respectively, on the even shells. A compact form of formulation for the QA is obtained in the standard-random approach which can easily be reduced to ternary alloy (TA) and mixed-spin models by the appropriate values of the random variables p; q and r. The phase diagrams are calculated on the temperature and ratio of bilinear interaction parameter planes for given values of probabilities.