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Ultrametricity in the Edwards-Anderson Model

P. Contucci·C. Giardina'·C. Giberti·G. Parisi·C. Vernia
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Abstract

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.

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P. Contucci, C. Giardina', C. Giberti, G. Parisi, C. Vernia. 2007-06-15. Ultrametricity in the Edwards-Anderson Model. https://doi.org/10.1103/physrevlett.99.057206

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