Fluctuation Bounds For Interface Free Energies in Spin Glasses

Abstract

We consider the free energy difference restricted to a finite volume for certain pairs of incongruent thermodynamic states (if they exist) in the Edwards-Anderson Ising spin glass at nonzero temperature. We prove that the variance of this quantity with respect to the couplings grows proportionally to the volume in any dimension greater than or equal to two. As an illustration of potential applications, we use this result to restrict the possible structure of Gibbs states in two dimensions.

arXiv comment19 pages, 0 figures

References in corpus (7)

• The metastate approach to thermodynamic chaos
• Spatial Inhomogeneity and Thermodynamic Chaos
• Uniqueness of Ground States for Short-Range Spin Glasses in the Half-Plane
• Are There Incongruent Ground States in 2D Edwards-Anderson Spin Glasses?
• Interfaces (and Regional Congruence?) in Spin Glasses
• Free energy fluctuations in Ising spin glasses
• Short-range spin glasses and Random Overlap Structures

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• Overlap Structure and Free Energy Fluctuations in Short-Range Spin Glasses
• Free Energy Difference Fluctuations in Short-Range Spin Glasses
• Critical Droplets and Replica Symmetry Breaking
• Haake-Lewenstein-Wilkens approach to spin-glasses revisited