{\cal O}
T                                       \label{43}$$

Notice that Eq.(\[10\]) is a particular case of this equation if choose [O]{} to be the Hamiltonian $H$.

In so far we have not made use of the all important concept of the block, but a practical implementation of the VRG or ERG methods does require it. The central role played by this concept makes all the real-space RG-methods to be block methods.

Once we have established the main features of the RG-program, there is quite freedom to implement specifically these fundamentals. We may classify this freedom in two aspects:

-   The choice of how to reduce the size of the lattice.

-   The choice of how many states to be retained in the truncation procedure.

We shall address the first aspect now. There are mainly two procedures to reduce the size of the lattice:

-   by dividing the lattice into blocks with $n_s$ sites each. This is the blocking method introduced by Kadanoff to treat spin lattice systems.

-   by retrieving site by site of the lattice at each step of the RG-program. This is the procedure used by Wilson in his RG-treatment of the Kondo problem. This method is clearly more suitable when the 