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

Ferromagnetic transition in three-dimensional double-exchange models is studied by the Monte Carlo method. Critical temperature $T_{\mathrm{c}}$ is precisely determined by finite-size scaling analysis. Strong spin fluctuations in this itinerant system significantly reduce $T_{\mathrm{c}}$ from mean-field estimates. By choosing appropriate parameters, obtained values of $T_{\mathrm{c}}$ quantitatively agree with experiments for the ferromagnetic metal regime of (La,Sr)MnO${}_3$, which is a typical perovskite manganite showing colossal magnetoresistance. This indicates that the double-exchange mechanism alone is sufficient to explain $T_{\mathrm{c}}$ in this material. Critical exponents are also discussed.