The phase diagrams of the ±K±K model on the Bethe lattice

•Biquadratic interaction K is randomized in a bimodal form with probabilities p   and 1−p1−p.•The attractive (K>0K>0) and the repulsive (K<0K<0) bimodal random distribution is used.•Calculations are carried out on the Bethe lattice with coordination number equal to 4.

The biquadratic exchange interaction is randomized in a bimodal form with probabilities (p  ) and (1−p1−p) for the cases with K>0K>0 (attractive case) and K<0K<0 (repulsive case), respectively, and its effects on the phase diagrams of the spin-1 Blume–Emery–Griffiths model are studied on the Bethe lattice by using the recursion relations. It was found that the critical behaviors of the model change drastically.