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• Critical properties of Fe-Al alloys in the bcc phase – phase diagram. • Ising model with exchange and superexchange interactions. • Monte Carlo simulations taking the effects of the Al cluster sizes. A spin-1/2 Ising model, defined in the body centered cubic lattice, is used to describe some of the thermodynamic properties of Fe p - Al q alloys, with p + q = 1. The model assumes, besides the nearest-neighbor exchange coupling, the existence of further next-nearest-neighbor superexchange interactions, where the latter ones depend on the aluminum atoms cluster size. The Ising system so considered is studied by employing Monte Carlo simulations, using a hybrid algorithm consisting of one single-spin Metropolis move together with one single-cluster Wolff algorithm allied, in addition, with single histograms procedures and finite-size scaling techniques. Quite good fits to the experimental results of the ordering critical temperature, as a function of Al concentration in the range 0 ⩽ q < 0.7 , are obtained and compared to more recent theoretical approaches done on the same alloys. [ABSTRACT FROM AUTHOR]