Uniqueness of Ground States for Short-Range Spin Glasses in the Half-Plane

Abstract

We consider the Edwards-Anderson Ising spin glass model on the half-plane $Z\times Z^{+}$ with zero external field and a wide range of choices, including mean zero Gaussian, for the common distribution of the collection J of i.i.d. nearest neighbor couplings. The infinite-volume joint distribution $K(J,\alpha )$ of couplings J and ground state pairs $\alpha$ with periodic (respectively, free) boundary conditions in the horizontal (respectively, vertical) coordinate is shown to exist without need for subsequence limits. Our main result is that for almost every J, the conditional distribution $K(\alpha |J)$ is supported on a single ground state pair.

20 pages, 3 figures

References in corpus (2)

• Theory of minimum spanning trees I: Mean-field theory and strongly disordered spin-glass model
• Theory of minimum spanning trees II: exact graphical methods and perturbation expansion at the percolation threshold

Cited by in corpus (18)

• Short-range Ising spin glasses: the metastate interpretation of replica symmetry breaking
• Which measures of spin-glass overlaps are informative?
• 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
• A Relation between Disorder Chaos and Incongruent States in Spin Glasses on ${\mathbb{Z}}^d$
• Zero-Temperature Fluctuations in Short-Range Spin Glasses
• Uniqueness of zero-temperature metastate in disordered Ising ferromagnets
• Extremal decomposition for random Gibbs measures: From general metastates to metastates on extremal random Gibbs measures
• Critical Droplets and Replica Symmetry Breaking
• Free Energy Difference Fluctuations in Short-Range Spin Glasses
• Triviality of the ground-state metastate in long-range Ising spin glasses in one dimension
• Busemann functions and infinite geodesics in two-dimensional first-passage percolation
• Gibbs-non Gibbs transitions in different geometries: The Widom-Rowlinson model under stochastic spin-flip dynamics
• Absence of replica symmetry breaking in the Edwards-Anderson model near zero temperature
• 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
• Absence of Disorder Chaos for Ising Spin Glasses on ${\mathbb{Z}}^d$