4 parallel paths, may represent better approximations and in some cases, one may obtain precise estimates when compared to those known for Bravais lattices; this motivates the study of SG models on such lattices. In spite of this, only a few works have considered Ising SGs on hierarchical lattices different from those of the MK family [19, 23, 25–28] and some of them have yielded important and stimulating results: (i) Studies on a special hierarchical lattice with fractal dimension D = 2 led to an estimate for the stiffness exponent y [19] ( y = − 1 /ν , where ν is the exponent associated with the divergence of the correlation length at zero temperature) in agreement with those obtained from other, more time-consuming, numerical approaches on a square lattice. An analysis of the ± J Ising SG model [25] on the same hierarchical lattice gave a ferromagnetic-paramagnetic critical frontier that should be a good approximation for the one of the corresponding model on a square lattice; (ii) Estimates of locations of multicritical points for SGs on some non-MK hierarchical lattices are in very good agreement with other numerical results on Bravais lattices, as well as with a conjecture based on gauge theory [25, 27]. In the present work we investigate Ising SGs defined on WB hierarchical lattices through the Hamiltonian, The lattices generated by the cells shown in Figs. 1(a), (b), and (c) present fractal di- mensions D = 2 . 32 , 3 . 58 , and 4 . 81; one should remind that these cells may be obtained from simple constructions of parts of Bravais lattices, namely, the square, cubic and four- dimensional hypercubic lattices, respectively [14]. The { J$_{ij}$ } denote random couplings between two spins located at nearest-neighboring sites i and j of this hierarchical lattice and may follow either the Gaussian, or bimodal ( ± J ) distributions, H = − ∑ <ij> J$_{ij}$S$_{i}$S$_{j}$ ( S$_{i}$ = ± 1) . (1) P ( J$_{ij}$ ) = 1 √$_{2}$$_{πJ}$ 2 exp [$_{−}$ ( J$_{ij}$ − J$_{0}$ ) 2 2 J 2 ] , (2) P ( J$_{ij}$ ) = p δ ( J$_{ij}$ − J ) + (1 − p ) δ ( J$_{ij}$ + J ) . (3)