Critical Temperature of Ferromagnetic Transition in Three-Dimensional Double-Exchange Models

Ferromagnetic transition in three-dimensional double-exchange models is studied by Monte Carlo method. Critical temperature $T_{\rm c}$ is precisely determined by the finite-size scaling analysis. Strong spin fluctuations in this itinerant system significantly reduce $T_{\rm c}$ from mean-field estimates. Obtained values of $T_{\rm c}$ quantitatively agree with experiments for La$_{1-x}$Sr$_{x}$MnO$_{3}$ which is a typical perovskite manganite showing the colossal magnetoresistance. This indicates that the double-exchange mechanism alone is sufficient to explain the ferromagnetic transition in this material. Critical exponents are also discussed.