  This work presents a Monte Carlo study of the phase transition in the
perovskites La$_{0.7}$Sr$_{0.3}$Mn$_{0.7}^{3+}$Mn$_{0.3-x}^{4+}$Ti$_x$O$_3$
($x$= 0.1, 0.2, and 0.25). 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. Fitting the experimental Curie temperature at $x=0$,
we estimated values of various exchange interactions in the system. The
dominant one is that between Mn$^{3+}$ and Mn$^{4+}$ which is at the origin of
the ferromagnetic ordering. Effects of the very small interaction $J\_2$
between NN Mn$^{3+}$ is analyzed: we show that it can cause an
antiferromagnetic phase above $T\_c$ which disappears at smaller $J\_2$ or at
Mn$^{3+}$ concentrations smaller than 0.55. Our results show a good agreement
with experiments on the magnetizations for substitution concentration $x=0.1$,
0.2 and 0.3. We also studied the applied-field effect on the magnetization and
our obtained results are compared with experiments performed at $x=10\%$.
