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Experimental data obtained with the perovskite compoundsPr$_{0.55}$Sr$_{0.45}$MnO$_{3}$ show that the magnetization decreases withincreasing temperature $T$ and undergoes a very sharp phase transition to theparamagnetic phase. The sharp transition in a system with a strong disorder isvery rare, if not non-existent, in the theory of phase transition in systems ofshort-range pairwise exchange interactions. To understand this remarkableproperty, we introduce a model including a multispin (cluster-like) interactionbetween Mn ions, in addition to the usual pairwise exchange terms between theseions and the Mn-Pr interactions. We carry out Monte Carlo (MC) simulations. Dueto 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 withdifferent spin models and various Hamiltonians, we find that the many-stateIsing spin model reproduces most of the experimental results. For theHamiltonian, we find that pairwise interactions alone between ions cannotreproduce the sharp transition and the magnetization below $T_C$. We have toinclude a multispin interaction as said above. We fit the MC results withexperimental data, and we estimate values of various exchange interactions inthe system. These values are found to be in the range of those found inperovskite manganite compounts. We also study the applied-field effect on themagnetization in the temperature region below and above the transitiontemperature $T_C$. We calculate the magnetic entropy change $|\Delta S_m|$ andthe Relative Cooling Power, for magnetic field from 1 to 3 Tesla. Oursimulation results are in good agreement with experiments.

Phase Transition and Magneto-caloric Properties of Perovskites Pr$_{0.55}$Sr$_{0.45}$MnO$_{3}$: Modeling versus Experiments