9 Hierarchical k$_{B}$T$_{c}$/J J$_{0}$/J Multicritical Point lattice ( J$_{0}$ = 0) ( T = 0) Cell 1(b) 0 . 980(2) 0 . 5665(5) ( k$_{B}$T$_{c}$/J ) = 1 . 690(2); ( J$_{0}$/J ) = 0 . 538(2) Cell 1(c) 2 . 35(1) 0 . 374(3) ( k$_{B}$T$_{c}$/J ) = 2 . 77(1); ( J$_{0}$/J ) = 0 . 35(1) TABLE I: Values of typical critical points in the phase diagrams of the Ising SG, on the hier- archical lattices defined by unit cells of Figs. 1(b) and 1(c), for couplings following a Gaussian distribution [Eq. (2)]: critical temperature for a symmetric distribution, zero-temperature criti- cal point separating phases SG and F , and coordinates of the multicritical point where the three critical frontiers meet. The error bars refer to the usual approach to criticality characteristic of the RG technique. We have also computed the zero-temperature stiffness exponent y for the phase diagram of Fig. 4(a). As expected, a positive value, y = 0 . 297 ± 0 . 003, signals a SG phase at finite temperatures; furthermore, this estimate is universal for all values of J$_{0}$ within the SG phase. This value is close to the recent one obtained for a MK lattice of fractal dimension D = 3 ( y ≈ 0 . 27 [13]), but it is slightly larger than those for the cubic lattice, y = 0 . 19 ± 0 . 01 [8] and y = 0 . 20 ± 0 . 05 [13]. The phase diagrams for the hierarchical lattice defined by the unit cell of Fig. 1(c), for couplings following either initial Gaussian of bimodal distributions, are qualitatively similar to those shown in Figs. 4(a) and 4(b), respectively. Values of typical critical points in these phase diagrams are given explicitly in Tables I and II. The higher complexity of this lattice generates larger errors in the numerical estimates; however, the points in such phase diagrams were computed with at least a one-decimal-digit certainty (error bars on second decimals). In particular, one should mention the estimates of the critical temper- atures for symmetric distributions, namely, ( k$_{B}$T$_{c}$/J ) = 2 . 35(1) and ( k$_{B}$T$_{c}$/J ) = 2 . 515(2), which are about 25% above those obtained from Monte Carlo simulations for the four- dimensional hypercubic lattice, i.e., ( k$_{B}$T$_{c}$/J ) ≈ 1 . 80, for the Gaussian distribution [37], and ( k$_{B}$T$_{c}$/J ) ≈ 2 . 00, for the bimodal distribution [38], respectively. These overestimates are consistent with the fact that the fractal dimension of the lattice considered herein is well above four ( D ≈ 4 . 81). Although we are not aware of numerical simulations carried