Ultrametricity in the Edwards-Anderson Model
  We test the property of ultrametricity for the spin glass three-dimensional Edwards-Anderson model in zero magnetic field with numerical simulations up to $20^3$ spins. We find an excellent agreement with the prediction of the mean field theory. Since ultrametricity is not compatible with a trivial structure of the overlap distribution our result contradicts the droplet theory. 
P. Contucci, C. Giardina', C. Giberti, G. Parisi, C. Vernia