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 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 that has not been used in this context so far. Being devised to account spin fluctuations explicitly, the latter method shows the best fit to experimental results.
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