On the origin of ultrametricity

In this paper we show that in systems where the probability distribution of the overlap is nontrivial in the infinite volume limit, the property of ultrametricity can be proved, in general, starting from two very simple and natural assumptions: each replica is equivalent to the others (replica equivalence or stochastic stability) and all the mutual information about a pair of equilibrium configurations is encoded in their mutual distance or overlap (separability or overlap equivalence).