We develop a systematic approach to perform real space renormalization
group transformations of the ''decimation type'' using perturbation t
heory. This type of transformations beyond d = 1 is non-trivial even f
or the Gaussian model on the lattice, Such a transformation is constru
cted on a hypercubic lattice in arbitrary dimensions, and perturbation
theory for spin models is developed around it. We check the formalism
on the solvable O(N) symmetric Heisenberg chain. The decimations are
especially useful to study models undergoing a continuous phase transi
tion at zero temperature, Results for one class of such models, the D
= 2 O(N) symmetric classical spins (N greater than or equal to 3) for
decimation with scale factor eta = 2 (when one quarter of the points i
s left), are presented.