Lack of Ultrametricity in the Low-Temperature phase of 3D Ising Spin Glasses

Abstract

We study the low-temperature spin-glass phases of the Sherrington-Kirkpatrick (SK) model and of the 3-dimensional short range Ising spin glass (3dISG). For the SK model, evidence for ultrametricity becomes clearer as the system size increases, while for the short-range case our results indicate the opposite, i.e. lack of ultrametricity. Our results are obtained by a recently proposed method that uses clustering to focus on the relevant parts of phase space and reduce finite size effects. Evidence that the mean field solution does not apply in detail to the 3dISG is also found by another method which does not rely on clustering.

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• Some considerations of finite dimensional spin glasses
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• Ultrametric probe of the spin-glass state in a field
• Cluster formation in complex multi-scale systems
• Equilibrium of disordered systems : constructing the appropriate valleys in each sample via strong disorder renormalization in configuration space
• Solution-space structure of (some) optimization problems
• Spin-glass dynamics: experiment, theory and simulation
• Pair correlation function for spin glasses
• Spin-glass chain in a magnetic field : influence of the disorder distribution on ground state properties and low-energy excitations
• Ultrametricity of optimal transport substates for multiple interacting paths over a square lattice network
• The Effect of Pure State Structure on Nonequilibrium Dynamics
• Probability Theory in Statistical Physics, Percolation, and Other Random Topics: The Work of C. Newman