The mixed spin-1/2 and spin-1 Blume–Capel model with random crystal field on the Bethe lattice: Two approaches

The effects of a random crystal field (RCF) on the phase diagrams of the mixed spin-1/2 and spin-1 Blume–Capel model are studied in terms of the recursion relations on the Bethe lattice for the coordination number z=6. The form of the RCF distribution is given in a bimodal form as P ( Δ j ) = p δ ( Δ j − Δ ) + ( 1 − p ) δ ( Δ j ) and its effects are examined on the phase diagrams by using two different approaches: (i) The site-dependent random case and (ii) The standard random case. The phase diagrams are obtained by the two approaches on the ( Δ , kT / J ) planes for given values of probability p from 0 to 1 with the increment of Δ p = 0.1 . Then, the obtained phase diagrams are compared to point out the differences and the effects of randomness are discussed.