Abstract
A model of the spontaneous ferromagnetic ordering in the ${\mathrm{La}}_{1\ensuremath{-}x}{\mathrm{Ca}}_{x}{\mathrm{MnO}}_{3}$ $(x\ensuremath{\approx}0.2--0.33)$ crystals is described. The partition function of the ferromagnetic to paramagnetic phase transition is determined, and the Curie temperature ${T}_{C}$ is expressed in terms of the two parameters. The parameters describe the binding energy of the ${e}_{g}$ electrons between two neighboring Mn ions and the Jahn-Teller energy of ${e}_{g}$ electron. Since at a temperature close to ${T}_{C}$ the partition function undergoes an abrupt drop, the crystal exhibits unusual changes in its properties at this temperature. The change of the specific-heat capacity, ${C}_{V},$ is calculated. The isotope shift of the critical temperature upon substitution of ${}^{16}\mathrm{O}$ by ${}^{18}\mathrm{O}$ is also calculated. The influence of the magnetic field on the resistivity is discussed.
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