A unified stability property in spin glasses

Abstract

Gibbs' measures in the Sherrington-Kirkpatrick type models satisfy two asymptotic stability properties, the Aizenman-Contucci stochastic stability and the Ghirlanda-Guerra identities, which play a fundamental role in our current understanding of these models. In this paper we show that one can combine these two properties very naturally into one unified stability property.

References in corpus (5)

• Broken Replica Symmetry Bounds in the Mean Field Spin Glass Model
• Characterization of invariant measures at the leading edge for competing particle systems
• Spin glass models from the point of view of spin distributions
• Stability of the Spin Glass Phase under Perturbations
• Random Overlap Structures: Properties and Applications to Spin Glasses

Cited by in corpus (5)

• The Sherrington-Kirkpatrick model: an overview
• PDE/statistical mechanics duality: relation between Guerra's interpolated $p$-spin ferromagnets and the Burgers hierarchy
• Notes on the polynomial identities in random overlap structures
• Spin glass polynomial identities from entropic constraints
• A new representation of the Ghirlanda-Guerra identities with applications