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A self-consistent (SC) renormalization group approach of the effective mediumkind has been developed and applied to the solution of the Ising model (IM). Arenormalization group equation in the local potential approximation (LPA)derived previously for spatially homogeneous systems has been extended to thelattice case and supplemented with a self-consistency condition on the paircorrelation function. To validate the approach it has been applied to thesimple cubic IM and good agreement of the spontaneous magnetization calculatedwith the use of the SC-LPA equation with the available exact Monte Carlosimulations data has been established. Next the approach has been applied tothe bcc IM corresponding to $\beta$-brass. With the use of the effective pairinteraction parameters from available {\em ab initio} calculations the criticaltemperature, the correlation length and the long range order parameter in thevicinity of the critical point have been calculated in excellent agreement withexperimental data. Qualitative and quantitative arguments have been given insupport of the suggestion that the experimentally observed decrease of theeffective critical exponent of the order parameter in comparison with theuniversal value is enhanced by the positive value of the second neighbour pairinteraction found in the {\em ab initio} calculations.

Self-consistent renormalization group approach to continuous phase transitions in alloys. Application to ordering in $\beta$-brass