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We take into accountnearest-neighbor (NN) interactions between magnetic ions Mn$^{3+}$($S=2$) and Mn$^{4+}$($S=3/2$) using a spin model describing a strong anisotropy on the $z$ axis. We have calculated the uniform and staggered magnetizations as well as the Edwards-Anderson order parameter as functions of temperature, with and without an applied magnetic field. 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