  In this paper we develop a general theory which provides a unified treatment
of two apparently different problems. The weak Gibbs property of measures
arising from the application of Renormalization Group maps and the mixing
properties of disordered lattice systems in the Griffiths' phase. We suppose
that the system satisfies a mixing condition in a subset of the lattice whose
complement is sparse enough namely, large regions are widely separated. We then
show how it is possible to construct a convergent multi-scale cluster
expansion.
