Paramagnetic-ferromagnetic transition in a double-exchange model

We study paramagnetic - ferromagnetic transition due to exchange interaction between classical localized magnetic moments and conduction electrons. We formulate the Dynamical Mean Field Approximation equations for arbitrary electron dispersion law, concentration and relation between exchange coupling and the electron band width. Solving these equations we find explicit formula for the transition temperature $T_c$. We present the results of calculations of the $T_c$ for the semi-circular electron density of states.