correct line of critical points that the exact model has. Moreover, the qRG equations for the renormalized spin operators show the appearence of a novel feature: [*the quantum group anomaly*]{}. In Sect. 5 we apply the qRG method to another model, the Ising model in a transverse field (ITF model). Here, the qRG-flow equations coincide with the tensor product decomposition of cyclic irreps of $SU_q(2)$ with $q^4=1$. Sect.6 is devoted to conclusions and prospectives.

A Brief Review of Block Renormalization Group Methods (BRG)
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In this section the block renormalization group method is revisited and we present a new and unified reformulation of it based on the idea of the [*intertwiner operator*]{} $T$ to be discussed below. For a more extensive account on this method we refer to [@jullienlibro] and chapter 11 of reference [@jaitisi] and references therein.

The block RG-method is a real-space RG-method introduced and developed by the SLAC group [@drell]. Let us recall that Wilson developed his numerical real-space renormalization group procedure to solve the Kondo problem [@wilson]. It was clear from the beginning that one could not hope to achieve the accuracy Wilson obtained for the Kondo problem when dealing with more complicated many-body quantum Hamiltonians 