Before introducing *block spin transformations* in chapter four of Random Walks, Critical Phenomena and Triviality in Quantum Field Theory, the authors state the following:

"In this chapter we sketch a specific method for constructing scaling (continuous) limits $G^{*}(x_{1},...,x_{n})$ of reescaled correlations $G_{\theta}(x_{1},...,x_{n})$ as $\theta \to \infty$, namely the Kadanoff block spin transformations. They serve as a typical example of "renormalization group transformations". Of course there are many other incarnations of the renormalization group strategy [...]."

Well, as the name suggests, the aim of the book is to address QFT but some of these techniques are also applicable and useful to rigorous statistical mechanics. For instance, I think more useful to statistical mechanics is the infinite volume limit than the continuum limit.

What are the most important "incarnations" of the renormalization group strategy in statistical mechanics? To what types of problems they fit and what are their limitations? Are they all related?