3 being constructed up to a given N -th hierarchy ( N ≫ 1). Although the RG may not be considered in general as an exact procedure for random systems on hierarchical lattices, it is expected to represent a good approximation, since in many cases, pure systems appear as particular limits of some random models. In the particular case of Ising SGs, the hierarchical lattices have been a very useful tool [5, 8, 13, 15–28], essentially due to the possibility of performing relatively low-time-consuming numerical computations. A significant gain in the computational time in the study of SGs represents the main advantage of the hierarchical lattices with respect to Monte Carlo simulations performed on Bravais lattices. In fact, one may obtain whole phase diagrams for non-symmetric distributions of the couplings (e.g., by changing the probability p of a bimodal distribution) within typically, a few computation hours of a standard desk computer; on the other hand, the criticality of a given particular case (e.g., the study of the case p = 1 / 2 of the bimodal distribution for the couplings) through Monte Carlo simulations may require several days on high-performance computer networks. The Migdal-Kadanoff (MK) family of hierarchical lattices [29, 30] have been widely explored, essentially due to the fact that its basic cell is formed by one-dimensional parallel paths each with a given scaling factor b ; its fractal dimension may be varied either by changing the scaling factor, or by a simple operation of adding more paths to the cell. As a consequence, most of the hierarchical-lattice SG studies so far were concentrated on these lattices [5, 8, 13, 15–18, 20–22, 24]. In spite of its simplicity, some of the results obtained in these lattices are quite impressive: (i) The bounds for the lower critical dimension, which is accepted nowadays to be greater than 2, but smaller than 3, were obtained on MK lattices [5] about a decade before their confirmation through distinct numerical investigations [6–9]. In fact, the lower critical dimension on MK lattices was estimated to be very close to 2 . 50 [17]; (ii) The SG critical-temperatures on the MK hierarchical lattice of fractal dimension D = 3, for symmetric Gaussian and bimodal distributions [5], present relative discrepancies of about 4%, taking into account the error bars, when compared with the recent estimates from Monte Carlo simulations on a cubic lattice [11]. However, the MK lattices represent the simplest types of hierarchical lattices and some of its results may be quantitatively poor approximations to well-known estimates on Bravais lattices. Other hierarchical lattices, which present connections between such