Ferromagnetic transition in a double-exchange system with alloy disorder

We study ferromagnetic transition in three-dimensional double-exchange model containing impurities. The influence of both spin fluctuations and impurity potential on conduction electrons is described in coherent potential approximation. In the framework of thermodynamic approach we construct Landau functional for the system "electrons (in disordered environment) + core spins". Analyzing the Landau functional we calculate the temperature of ferromagnetic transition $T_C$ and paramagnetic susceptibility $\chi$. For $T_C$, we thus extend the result obtained by Furukawa in the framework of the Dynamical Mean Field Approximation, with which our result coincides in the limit of zero impurity potential. We find, that the alloy disorder, able to produce a gap in density of electron states, can substantially decrease $T_C$ with respect to the case of no impurities. We also study the general relation between the Coherent Potential Approximation and the Dynamical Mean Field Approximation.