lattice is one-dimensional.

We shall be dealing with the Kadanoff block methods mainly because they are well suited to perform analytical computations and because they are conceptually easy to be extended to higher dimensions. On the contrary, the DMRG method introduced by White [@white] works with the Wilsonian numerical RG-procedure what makes it intrinsically one-dimensional and difficult to be generalized to more dimensions.

The first step of the BRG method consists in asembling the set of lattice points into diconnected blocks of $n_s$ sites each.

In this fashion there are a total of $N'=N/n_s$ blocks in the whole chain. This partition of the lattice into blocks induces a decomposition of the Hamiltonian (\[1\]) into an intrablock Hamiltonian $H_B$ and a interblock Hamiltonian $H_{BB}$:

$$H = H_B + \lambda H_{BB}                    \label{21}$$

where $\lambda $ is a coupling constant which is already present in $H$ or else it can be introduced as a parameter characterizing the interblock coupling and in this latter case one can set it to one at the end of the discussion.

Observe that the block Hamiltonian $H_B$ is a sum of commuting Hamiltonians each acting on every block. The diagonalization of $H_s$ can thus be achieved for small 