A systematic study of the magnetic properties of the manganitesLn0.5(A,A′)0.5MnO3(A,A′=Ba,Ca, Sr) has been carried out. The variations ofTCandTNvs two parameters, the average size of the interpolated cations⟨rA⟩and the mismatch effect represented by the variance&sgr;2,have been studied for the series of manganitesLa0.5(A,A′)0.5MnO3,Pr0.5(A,A′)0.5MnO3,Nd0.5(A,A′)0.5MnO3andSm0.5(A,A′)0.5MnO3(A,A′=Ba,Ca, Sr), involving at most three different cations on the perovskite A site. The results obtained for other(Ln, Ln′)0.5Sr0.5MnO3(Ln, Ln′=Gd, Sm Y, Pr)have been taken into consideration. A&sgr;2−⟨rA⟩diagram has been established, which displays the different types of magnetic behaviors that can be exhibited byLn0.5A0.5MnO3manganites, i.e., when the temperature is decreasing, either a paramagnetic (PM) to ferromagnetic (FM) transition, or PM to FM followed by FM to antiferromagnetic transitions, or a PM to weak ferromagnetic transition. ©1997 American Institute of Physics.