The $\pm J$ distribution in the mixed spin-$1/2$ and $5/2$ Blume–Capel model

Phase diagrams of the mixed spin-$1/2$ and $5/2$ Blume–Capel model on the Bethe lattice in the $\pm J$ distribution with probabilities $p$ and $1-p$ for $J>0$ and $J<0$ and the adjustment parameter $\alpha$ are obtained on the $(\alpha,T)$ and $(p, T)$ planes for given values of single-ion anisotropy $D$ by varying $p$ in the range $0\leq p\leq 1$ and $\alpha$ in the range $0\leq\alpha\leq 1$. The phase diagrams are constructed by studying the thermal variations of the order parameters in terms of exact recursion relations, and the probability distribution is then implemented into the model. The model presents first- and second-order phase transitions in addition to the tricritical and bicritical points for the coordination number $q=3$ corresponding to the honeycomb lattice.