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It is argued that cluster methods provide a viable alternative to Wilson'smomentum shell integration technique at the early stage of renormalization inthe field-theoretic models with strongly coupled fields because these methodsallow for systematic accounting of all interactions in the system irrespectiveof their strength. These methods, however, are restricted to relatively smallspatial scales, so they ought to be supplemented with more conventionalrenormalization-group (RG) techniques to account for large scale correlations.To fulfil this goal a "layer-cake" renormalization scheme earlier developed forrotationally symmetric Hamiltonians has been generalized to the lattice case.The RG technique can be naturally integrated with an appropriately modifiedcluster method so that the RG equations were used only in the presence of largescale fluctuations, while in their absence the approach reduced to aconventional cluster method. As an illustrative example the simplestsingle-site cluster approximation together with the local-potential RG equationare applied to simple cubic Ising model to calculate several non-universalquantities such as the magnetization curve, the critical temperature, and somecritical amplitudes. Good agreement with Monte Carlo simulations and seriesexpansion results was found.

Hybrid cluster+RG approach to the theory of phase transitions in strongly coupled Landau-Ginzburg-Wilson model