  A review of the Contractor Renormalization (CORE) method, as a systematic
derivation of the low energy effective hamiltonian, is given, with emphasis on
its differences and advantages over traditional perturbative (weak/strong
links) real space RG. For the low energy physics of the 2D Hubbard model, we
derive the plaquette bosons (projected SO(5)) model which connects the
microscopic model to phases and phenomenology of high-Tc cuprates. For the
S=1/2 Pyrochlore and Kagome antiferromagnets, the effective hamiltonians
predict spin-disordered, lattice symmetry breaking, ground states with a large
density of low energy singlets as found by exact diagonalization of small
clusters.
