2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/139284We 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.typos correctedDisordered Systems and Neural NetworksStatistical MechanicsMathematical Physicstext