Free-energy cost for ultrametricity violations in spin glasses

We apply the technique introduced in a previous paper, to study the violation of ultrametricity in a Spin Glass model. We consider 3 real replicas of a Spin Glass near the glassy temperature, constrained in such a way that their overlaps violate ultrametricity. We compute the free energy of such a system and find that the additional free energy required by the constraint is extensive (proportional to N), This result is likely to be independent of the model chosen, and to be a general feature in Mean-Field Spin Glass systems.