  Statistical systems near a classical critical point have been intensively
studied both from theoretical and experimental points of view. In particular,
correlation functions are of relevance in comparing theoretical models with the
experimental data of real systems. In order to compute physical quantities near
a critical point one needs to know the model at the critical (conformal) point.
In this line, recent progresses in the knowledge of conformal field theories,
through the conformal bootstrap, give the hope to get some interesting results
also outside of the critical point. In this note we will review and clarify
how, starting from the knowledge of the critical correlators, one can calculate
in a safe way their behavior outside the critical point. The approach
illustrated requires the model to be just scale invariant at the critical
point. We will clarify the method by applying it to different kind of
perturbations of the $2D$ Ising model.
