Existence of a renormalized Landau-Ginzburg theory

We assume that, when a is close to ac ((a — at.)b2l(d ) 1) the system, which then belongs to the critical domain, can be described by a limiting theory. In fact, the existence of this theory can be proved by perturbation in the vicinity of d = 4.17 The physical quantities, in this limit, are the renormalized Green s functions (ri,.. ., rp) which by definition are proportional to the Green s functions ( . rp a). We have 

We can associate renormalized vertex functions with the renormalized Green s functions, by proceeding as was done in Chapter 11, Section 5.2.2. It is easy to verify that 

In order to define a theory that remains finite when a - ac, we have of course to express the renormalized vertex functions in terms of quantities having a physical meaning, and we shall study this point below more precisely. 

---