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Experimental data obtained with the perovskite compounds
Pr$_{0.55}$Sr$_{0.45}$MnO$_{3}$ show that the magnetization decreases with
increasing temperature $T$ and undergoes a very sharp phase transition to the
paramagnetic phase. The sharp transition in a system with a strong disorder is
very rare, if not non-existent, in the theory of phase transition in systems of
short-range pairwise exchange interactions. To understand this remarkable
property, we introduce a model including a multispin (cluster-like) interaction
between Mn ions, in addition to the usual pairwise exchange terms between these
ions and the Mn-Pr interactions. We carry out Monte Carlo (MC) simulations. Due
to the doping, Mn$^{4+}$ with $S=3/2$ has the concentration of Pr$^{3+}$
($S=1$) and Mn$^{3+}$ with $S=2$ has the Sr concentration. After attempts with
different spin models and various Hamiltonians, we find that the many-state
Ising spin model reproduces most of the experimental results. For the
Hamiltonian, we find that pairwise interactions alone between ions cannot
reproduce the sharp transition and the magnetization below $T_C$. We have to
include a multispin interaction as said above. We fit the MC results with
experimental data, and we estimate values of various exchange interactions in
the system. These values are found to be in the range of those found in
perovskite manganite compounts. We also study the applied-field effect on the
magnetization in the temperature region below and above the transition
temperature $T_C$. We calculate the magnetic entropy change $|\Delta S_m|$ and
the Relative Cooling Power, for magnetic field from 1 to 3 Tesla. Our
simulation results are in good agreement with experiments.