16 0 1 2 3 4 5 6 J$_{0}$/J 2 4 6 8 10 12 14 k B T/J P F FIG. 3: Phase diagram for an Ising SG on the hierarchical lattice defined by the unit cell of Fig. 1(a), with a Gaussian distribution for the couplings. FIG. 4: Phase diagrams of the Ising SG on the hierarchical lattice defined by the unit cell of Fig. 1(b): (a) Gaussian distribution for the couplings; (b) bimodal distribution for the couplings. 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 J$_{0}$/J 1 2 3 4 5 6 k B T/J SG F P (a) 0.5 0.6 0.7 0.8 0.9 1 p 0 1 2 3 4 5 6 k B T/J SG F P (b)