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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, 

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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, 

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