The magnetic behaviors of the Fe–Mn–Al alloy are simulated on the Bethe lattice by using a trimodal random bilinear exchange interaction(J) distribution in the Blume–Capel(BC) model. Ferromagnetic(J > 0) or antiferromagnetic(J < 0)bonds or dilution of the bonds(J = 0) are assumed between the atoms with some probabilities. It is found that the secondor the first-order phase boundaries separate the ferromagnetic(F), antiferromagnetic(AF), paramagnetic(P), or spin-glass(SG) phases from the possible other one. In addition to the tricritical points, the special points at which the second- and the first-order and the spin-glass phase lines meet are also found. Very rich phase diagrams in agreement with the literature are obtained. The magnetic behaviors of the Fe-Mn-Al alloy are simulated on the Bethe lattice by using a trimodal random bilinear exchange interaction (J) distribution in the Blume-Capel (BC) model. Ferromagnetic (J> 0) or antiferromagnetic (J < 0) bonds or dilution of the bonds (J = 0) are assume between the atoms with some probabilities. It is found that the secondor the first-order phase boundaries separate the ferromagnetic (F), antiferromagnetic (AF) In addition to the tricritical points, the special points at which the second- and the first-order and the spin-glass phase lines meet also one. diagrams in agreement with the literature are obtained.