Ultrametricity in 3D Edwards-Anderson spin glasses

Abstract

We perform an accurate test of Ultrametricity in the aging dynamics of the three dimensional Edwards-Anderson spin glass. Our method consists in considering the evolution in parallel of two identical systems constrained to have fixed overlap. This turns out to be a particularly efficient way to study the geometrical relations between configurations at distant large times. Our findings strongly hint towards dynamical ultrametricity in spin glasses, while this is absent in simpler aging systems with domain growth dynamics. A recently developed theory of linear response in glassy systems allows to infer that dynamical ultrametricity implies the same property at the level of equilibrium states.

4 pages, 5 figures

References in corpus (8)

• Critical exponents of the three dimensional diluted Ising model
• Measuring equilibrium properties in aging systems
• Evidence for the droplet/scaling picture of spin glasses
• On the Phase Structure of the 3D Edwards Anderson Spin Glass
• Universality in the off-equilibrium critical dynamics of the $3d$ diluted Ising model
• Small Window Overlaps Are Effective Probes of Replica Symmetry Breaking in 3D Spin Glasses
• On the Dynamics of the 4d Spin Glass in a magnetic field
• Are Ground States of 3d +/-J Spin Glasses ultrametric ?

Cited by in corpus (11)

• Boosting Monte Carlo simulations of spin glasses using autoregressive neural networks
• Ultrametricity in the Edwards-Anderson Model
• Lack of Ultrametricity in the Low-Temperature phase of 3D Ising Spin Glasses
• Ultrametricity and clustering of states in spin glasses: A one-dimensional view
• Is dynamic ultrametricity observable in spin glasses?
• Some considerations of finite dimensional spin glasses
• State Hierarchy Induced by Correlated Spin Domains in short range spin glasses
• Spin glasses and algorithm benchmarks: A one-dimensional view
• Ultrametric probe of the spin-glass state in a field
• A Quantitative Clustering Approach to Ultrametricity in Spin Glasses
• Dynamic ultrametricity in finite dimensional spin glasses