  We provide a systematic analysis of finite-temperature magnetic properties of
random alloys Fe$_x$Ni$_{1-x}$ with the face-centered-cubic structure over a
broad concentration range $x$. By means of the spin-polarized relativistic
Korringa-Kohn-Rostoker method we calculate the electronic structure of
disordered iron-nickel alloys and discuss how a composition change affects
magnetic moments of Fe and Ni and the density of states. We investigate how the
Curie temperature depends on Fe concentration using conventional approaches,
such as mean-field approximation or Monte Carlo simulations, and dynamic
spin-fluctuation theory. Being devised to account for spin fluctuations
explicitly, the latter method shows the best fit to experimental results.
