Are There Incongruent Ground States in 2D Edwards-Anderson Spin Glasses?

Abstract

We present a detailed proof of a previously announced result (C.M. Newman and D.L. Stein, Phys. Rev. Lett. v. 84, pp. 3966--3969 (2000)) supporting the absence of multiple (incongruent) ground state pairs for 2D Edwards-Anderson spin glasses (with zero external field and, e.g., Gaussian couplings): if two ground state pairs (chosen from metastates with, e.g., periodic boundary conditions) on the infinite square lattice are distinct, then the dual bonds where they differ form a single doubly-infinite, positive-density domain wall. It is an open problem to prove that such a situation cannot occur (or else to show --- much less likely in our opinion --- that it indeed does happen) in these models. Our proof involves an analysis of how (infinite-volume) ground states change as (finitely many) couplings vary, which leads us to a notion of zero-temperature excitation metastates, that may be of independent interest.

18 pages (LaTeX); 1 figure; minor revisions; to appear in Commun. Math. Phys

Cited by in corpus (17)

• Ordering and Broken Symmetry in Short-Ranged Spin Glasses
• Strong disorder fixed points in the two-dimensional random-bond Ising model
• Uniqueness of Ground States for Short-Range Spin Glasses in the Half-Plane
• Thermodynamics and Universality for Mean Field Quantum Spin Glasses
• Fluctuation Bounds For Interface Free Energies in Spin Glasses
• Metastates in finite-type mean-field models: visibility, invisibility, and random restoration of symmetry
• Ground State Stability and the Nature of the Spin Glass Phase
• Zero-Temperature Fluctuations in Short-Range Spin Glasses
• Uniqueness of zero-temperature metastate in disordered Ising ferromagnets
• The Binomial Spin Glass
• Critical Droplets and Replica Symmetry Breaking
• Metastates in mean-field models with random external fields generated by Markov chains
• Free Energy Difference Fluctuations in Short-Range Spin Glasses
• Triviality of the ground-state metastate in long-range Ising spin glasses in one dimension
• Absence of Disorder Chaos for Ising Spin Glasses on ${\mathbb{Z}}^d$
• Probability Theory in Statistical Physics, Percolation, and Other Random Topics: The Work of C. Newman
• On the number of ground states of the Edwards-Anderson spin glass model