Small parameter for lattice models with strong interaction

Diagram series expansion for lattice models with a localized nonlinearity can be renormalized so that diagram vertexes become irreducible vertex parts of certain impurity model. Thus renormalized series converges well in the very opposite cases of tight and weak binding and pretends to describe in a regular way strong-correlated systems with localized interaction. Benchmark results for the classical O(N) models on a cubic lattice are presented.