Ultrametricity in the Edwards-Anderson Model
P. Contucci, C. Giardina', C. Giberti, G. Parisi, C. Vernia
TL;DR
This paper investigates ultrametricity in the 3D Edwards-Anderson spin glass model through numerical simulations, finding results that support mean field theory and challenge the droplet theory.
Contribution
It provides the first numerical evidence of ultrametricity in a finite-dimensional spin glass model, supporting mean field predictions.
Findings
Ultrametricity observed in the 3D Edwards-Anderson model.
Results align with mean field theory predictions.
Contradicts the droplet theory's trivial overlap structure.
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 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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Taxonomy
TopicsTheoretical and Computational Physics · Stochastic processes and statistical mechanics · Random Matrices and Applications