  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 $0\le q<0.7$, are obtained and compared to more
recent theoretical approaches done on the same alloys.
