8 a hierarchical lattice with fractal dimension D ≈ 3 . 58 and those of the cubic lattice, are justified by the fact that the cell of Fig. 1(b) may be obtained from a simple construction of a piece of the cubic lattice [14]. On the other hand, the critical temperature associated with the corresponding ferromagnetic Ising model, which may be obtained either from the p = 1 critical point separating phases P and F in Fig. 4(b), or by computing the slope of the critical frontier of Fig. 4(b) for ( J$_{0}$/J ) large, is given by ( k$_{B}$T$_{c}$/J$_{0}$ ) = 5 . 46 ± 0 . 01, which is somewhere in between the estimates of critical temperatures for the ferromagnetic Ising model on the cubic [( k$_{B}$T$_{c}$/J$_{0}$ ) ≈ 4 . 512] and the four-dimensional hypercubic lattice [( k$_{B}$T$_{c}$/J$_{0}$ ) ≈ 6 . 680], obtained from Monte Carlo simulations [33]. Another important aspect of the phase diagrams shown in Fig. 4 is a small reentrance effect in the region slightly to the right of the multicritical point; by lowering the temper- ature, one may go from a high-temperature disordered ( P ) phase to an ordered one ( F phase) and then, back to a more disordered ( SG ) phase at low temperatures. By compar- ing the coordinates of the multicritical points and the respective zero-temperature ones in Tables I and II, one sees that this effect, although very weak, is outside the error bars of the method. This is illustrated in Fig. 5, which shows the evolution of the average < K$_{ij}$ > with the RG step n , in the case of couplings following an initial Gaussian distribution, for typical values of J$_{0}$/J around the critical frontier separating the phases SG and F . In Fig. 5(a) one sees the behavior of < K$_{ij}$ > for a fixed temperature [( k$_{B}$T/J ) = 0 . 95], below the SG critical temperature, showing that for ( J$_{0}$/J ) = 0 . 556 one is still on the SG phase, whereas < K$_{ij}$ > diverges for ( J$_{0}$/J ) = 0 . 557, signalling a F phase. The same procedure is applied to zero temperature in Fig. 5(b), where one sees these two different types of behavior for ( J$_{0}$/J ) = 0 . 566 and ( J$_{0}$/J ) = 0 . 567, respectively. It should be mentioned that this type of reentrance phenomena has been observed experimentally, e.g., in Eu$_{x}$Sr$_{1}$$_{−}$$_{x}$S [34] and AuFe (14% Fe) [35]. Theoretically, it has been also found in the mean-field replica-symmetric solution (which turns out to be unstable at low temper- atures) of the Ising SG, although its correct solution, characterized by replica-symmetry breaking, has washed away the reentrance [1–3]. It is important to stress that reentrance phenomena on theoretical SG models are very subtle and difficult to be obtained numer- ically, in such a way that only a few works in the literature were able to capture such an effect so far (see, e.g., Refs. [25, 36]).