associated with the divergence of the correlation length, ξ ∼ T − $^{ν}$. We have computed y = − 0 . 290 ± 0 . 003, leading to ν = 3 . 45 ± 0 . 04, for all J$_{0}$ in the interval 0 ≤ ( J$_{0}$/J ) < 1 (cf. Fig. 3). This estimate coincides, within the error bars, with those obtained for the particular case J$_{0}$ = 0 in Ref. [19] for the same hierarchical lattice, as well as with several estimates for the square lattice, like y = − 0 . 291 ± 0 . 002 [8], y = − 0 . 287 ± 0 . 004 [31], and y = − 0 . 284 ± 0 . 004 [32]. Although the lattice considered herein presents a fractal dimension D ≈ 2 . 32, which is about 15% higher than the dimension of the square lattice, it has been much used in the literature as an approach for models on the later, essentially because it may be obtained through a simple construction from a piece of the square lattice, keeping one of its most important properties, the self-duality [14]. 

The phase diagram for the case of the hierarchical lattice defined by the unit cell of Fig. 1(a), with a bimodal distribution for the couplings, is qualitatively similar to the one already investigated in Ref. [25]. From the present analysis one concludes that the SG lower critical dimension in the WB hierarchical-lattice family should be greater than 2 . 32; this result is in agreement with calculations carried on MK lattices, where this lower critical dimension was estimated to be very close to 2 . 50 [17]. 

The phase diagrams for the hierarchical lattice defined by the unit cell of Fig. 1(b) are shown in Fig. 4, for couplings following the Gaussian distribution [Fig. 4(a)], or the bimodal distribution [Fig. 4(b)]. The coordinates of the most important critical points of these phase diagrams are given explicitly in Tables I and II. Similarly to the previous case, the points used in order to draw these phase diagrams were calculated from the standard narrowing RG procedure, with at least a two-decimal-digit certainty (error bars on third decimals). It is important to notice the estimates of the critical temperatures for symmetric distributions, namely, ( k$_{B}$T$_{c}$/J ) = 0 . 980(2) and ( k$_{B}$T$_{c}$/J ) = 1 . 112(2); these estimates are in very good agreement with recent results from Monte Carlo simulations on a cubic lattice, which yielded ( k$_{B}$T$_{c}$/J ) = 0 . 951(9) and ( k$_{B}$T$_{c}$/J ) = 1 . 120(4), for symmetric Gaussian and bimodal distributions, respectively [11]. Comparing the present results with those of Ref. [11], taking into account the error bars, one finds a relative discrepancy of about 2% in the Gaussian case, whereas for the symmetric bimodal distribution the two estimates essentially coincide (leading to a relative discrepancy of about 0 . 2%). Such good agreements on critical-temperature estimates, between those of 

