One possible approach to the study of the geometry of the Gibbs measure in the Sherrington-Kirkpatrick
type models (for example, the chaos and ultrametricity problems) is based on the analysis of the free energy
on several replicas of the system under some constraints on the distances between replicas. In general, this
approach runs into serious technical difficulties, but we were able to make some progress in the setting of the
spherical p-spin SK models where many computations become more explicit.