Nonrealistic Behavior of Mean Field Spin Glasses

Abstract

We study chaotic size dependence of the low temperature correlations in the SK spin glass. We prove that as temperature scales to zero with volume, for any typical coupling realization, the correlations cycle through every spin configuration in every fixed observation window. This cannot happen in short-ranged models as there it would mean that every spin configuration is an infinite-volume ground state. Its occurrence in the SK model means that the commonly used `modified clustering' notion of states sheds little light on the RSB solution of SK, and conversely, the RSB solution sheds little light on the thermodynamic structure of EA models.

5 pages (RevTeX); 1 figure; final published version

References in corpus (3)

• The Thermodynamic Limit in Mean Field Spin Glass Models
• Spin and link overlaps in 3-dimensional spin glasses
• Ordering and Broken Symmetry in Short-Ranged Spin Glasses

Cited by in corpus (7)

• Ordering and Broken Symmetry in Short-Ranged Spin Glasses
• Short-range Ising spin glasses: the metastate interpretation of replica symmetry breaking
• Thermodynamics and Universality for Mean Field Quantum Spin Glasses
• On the Ising model with random boundary condition
• Ground State Stability and the Nature of the Spin Glass Phase
• The free energy of a quantum Sherrington-Kirkpatrick spin-glass model for weak disorder
• Probability Theory in Statistical Physics, Percolation, and Other Random Topics: The Work of C. Newman