  A self-consistent (SC) renormalization group approach of the effective medium
kind has been developed and applied to the solution of the Ising model (IM). A
renormalization group equation in the local potential approximation (LPA)
derived previously for spatially homogeneous systems has been extended to the
lattice case and supplemented with a self-consistency condition on the pair
correlation function. To validate the approach it has been applied to the
simple cubic IM and good agreement of the spontaneous magnetization calculated
with the use of the SC-LPA equation with the available exact Monte Carlo
simulations data has been established. Next the approach has been applied to
the bcc IM corresponding to $\beta$-brass. With the use of the effective pair
interaction parameters from available {\em ab initio} calculations the critical
temperature, the correlation length and the long range order parameter in the
vicinity of the critical point have been calculated in excellent agreement with
experimental data. Qualitative and quantitative arguments have been given in
support of the suggestion that the experimentally observed decrease of the
effective critical exponent of the order parameter in comparison with the
universal value is enhanced by the positive value of the second neighbour pair
interaction found in the {\em ab initio} calculations.
