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A spin-1/2 Ising model, defined in the body centered cubic lattice, is usedto 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, theexistence of further next-nearest-neighbor superexchange interactions, wherethe latter ones depend on the aluminum atoms cluster size. The Ising system soconsidered is studied by employing Monte Carlo simulations, using a hybridalgorithm consisting of one single-spin Metropolis move together with onesingle-cluster Wolff algorithm allied, in addition, with single histogramsprocedures and finite-size scaling techniques. Quite good fits to theexperimental results of the ordering critical temperature, as a function of Alconcentration in the range $0\le q<0.7$, are obtained and compared to morerecent theoretical approaches done on the same alloys.

Cluster size effects in the magnetic properties of Fe$_p$-Al$_{q=1-p}$ alloys