P. Contucci, C. Giardina', C. Giberti, G. Parisi, C. Vernia
Published 2006-07-14, updated 2007-06-15Version 4
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.
Comments: typos corrected
Journal: Phys. Rev. Lett. 99, 057206 (2007)
Phase Transition in a Random Minima Model: Mean Field Theory and Exact Solution on the Bethe Lattice
Evidence of exactness of the mean field theory in the nonextensive regime of long-range spin models
On the origin of ultrametricity
