On the branching structure of the tree of states in spin glasses

We review some known results on the nature of the tree of states in spin glasses and we present new results on its topology. We pay particular attention to the so-called continuum limit in which the levels are labeled by a continuous variablex. We also study the dependence on the levelx of the type of branching (bifurcation, trifurcation,...). We show that the statistics of the tree is universal in the continuum limit, i.e., it does not depend on the details of the algorithm used to generate the tree.