We develop a formalism for performing real space renormalization group
transformations of the ''decimation type'' using perturbation theory.
The type of transformations beyond d = 1 is nontrivial even for free
theories. We check the formalism on solvable case of O(N) symmetric He
isenberg chain. The transformation is particularly useful to study asy
mptotically free theories, Results for one class of such models, the d
= 2 O(N) symmetric sigma models (N greater than or equal to 3) for de
cimation with scale factor eta = 2 (when quarter of the points is left
) are given as an example.