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

Abstract The biquadratic exchange interaction is randomized in a bimodal form with probabilities ( p ) and ( 1 − p ) for the cases with K > 0 (attractive case) and K 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.