Replica equivalence in the Edwards-Anderson model

Abstract

After introducing and discussing the "link-overlap" between spin configurations we show that the Edwards-Anderson model has a "replica-equivalent" quenched equilibrium state, a property introduced by Parisi in the description of the mean-field spin-glass phase which generalizes ultrametricity. Our argument is based on the control of fluctuations through the property of stochastic stability and works for all the finite-dimensional spin-glass models.

12 pages, few remarks added. To appear in Journal of Physics A: Mathematical and General

References in corpus (8)

• Measuring equilibrium properties in aging systems
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• On the Stability of the Quenched State in Mean Field Spin Glass Models
• The response of glassy systems to random perturbations: A bridge between equilibrium and off-equilibrium
• On the origin of ultrametricity
• Thermodynamical Limit for Correlated Gaussian Random Energy Models
• Comment on "Evidence for the Droplet/Scaling Picture of Spin Glasses"
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Cited by in corpus (16)

• Nature of the spin-glass phase at experimental length scales
• Spin-Glass Stochastic Stability: a Rigorous Proof
• Temperature chaos in 3D Ising Spin Glasses is driven by rare events
• Ultrametricity in the Edwards-Anderson Model
• Overlap Equivalence in the Edwards-Anderson Model
• Some considerations of finite dimensional spin glasses
• Cluster Percolation in the Two-Dimensional Ising Spin Glass
• Replica symmetric spin glass field theory
• Short-range spin glasses and Random Overlap Structures
• Stochastic Stability: a Review and Some Perspectives
• Factorization Properties in the 3D Edwards-Anderson Model
• Non-trivial link overlap distribution in three-dimensional Ising spin glasses
• Lack of monotonicity in spin glass correlation functions
• Spin Glass Identities and the Nishimori Line
• Cluster percolation in the three-dimensional $\pm J$ random-bond Ising model
• The Ghirlanda-Guerra Identities