The functional integral formalism which has been applied to the Ising model of ferromagnetism is used here to treat the interaction of the annealing process and magnetization in a dilute magnetic alloy AB (magnetic component A). Only the possibility of 50 50 component ordering is considered. A variational principle is derived which leads to an upper limit for the free energy of the model. The approximation obtained by minimizing this upper limit would appear to be an extension of the Horwitz-Callen theory.Order-disorder and magnetic transition curves are presented for three values of the ratio R of the spin-exchange energy to the mixing energy. Component ordering is found to inhibit the magnetic transition in alloys which are rich in component B.