2003/01/31 by C. M. Newman, Charles M. Newman, D. L. Stein · 1 citation
Economics, Econometrics and Finance · Physics and Astronomy · #Complex Network Analysis Techniques #Complex Systems and Time Series Analysis #Theoretical and Computational Physics #cond-mat.dis-nn #cond-mat.stat-mech
paper · pdf · doi:10.1103/physrevlett.91.197205
published as Physical Review Letters 91, 197205 (2003) · 5 pages (RevTeX); 1 figure; final published version
openalex publication_date 2003/11/06 · arxiv created 2003/11/12 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study chaotic size dependence of the low-temperature correlations in the Sherrington-Kirkpatrick (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 replica symmetry breaking (RSB) solution of SK, and, conversely, the RSB solution sheds little light on the thermodynamic structure of Edwards-Anderson models.