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Dividing the lattice into blocks with singlet ground state and knowing theexact low energy spectrum of the blocks and of dimers (or trimers) of blocks,it is possible to approach the lowest part of the lattice spectrum through anexcitonic type effective model. The potentialities of the method areillustrated on the 1-D frustrated chain and the 1/5-depleted square and theplaquette 2-D lattices. The method correctly locates the phase transitionsbetween gapped and non-gapped phases.Comment: Submitted for publication in Phys. Rev.

Renormalized excitonic method in terms of block excitations: Application to spin lattices