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