Chaos picture of spin glasses
Abstract
The chaos picture is a novel, coherent, and intuitive theoretical framework for spin glasses, reconciling the 40-year-old droplet vs. replica symmetry breaking debate. First, we argue the formation of a hierarchical energy landscape by pinning and dynamic filtering of random droplets. As the temperature decreases, the chaos picture describes a progressive freezing of scale-dependent droplets in real space, which mirrors a hierarchical free energy landscape fracturing process in phase space. This bifurcation process is accompanied by temperature chaos, leading to dynamic pure state coexistence without violating the droplet scaling. Crucially, the interface geometry is not critical to these mechanisms, naturally incorporating the interface crossover from planar, fractal, to space-filling as the dimensionality increases, in line with the mean-field limit. Finally, the chaos picture provides profound insights into spin-glass dynamics such as aging, rejuvenation, and memory effect, while offering a streamlined reinterpretation of the complex metastate framework.
Related
- Free energy of non-convex multi-species spin glasses with centered Ising spins
- Free energy of non-convex multi-species spherical spin glasses
- Free energy of spherical vector spin glasses
- A Universal Lower Bound for the Complexity of Gaussian-Divisible Spin Glasses
- Approximating the Gibbs Measure of Spherical Spin Glasses to Within o(N−1/2) in the Replica Symmetric Phase
BibTeX
@misc{wang2026chaos,
title = {{Chaos picture of spin glasses}},
author = {Wenlong Wang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.37426},
eprint = {2610.37426},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.37426},
}
RIS
TY - UNPB
TI - Chaos picture of spin glasses
AU - Wenlong Wang
PY - 2026
DA - 2026/10/27
PB - arXiv
DO - 10.48550/arxiv.2610.37426
UR - https://arxiv.org/abs/2610.37426
AB - The chaos picture is a novel, coherent, and intuitive theoretical framework for spin glasses, reconciling the 40-year-old droplet vs. replica symmetry breaking debate. First, we argue the formation of a hierarchical energy landscape by pinning and dynamic filtering of random droplets. As the temperature decreases, the chaos picture describes a progressive freezing of scale-dependent droplets in real space, which mirrors a hierarchical free energy landscape fracturing process in phase space. This bifurcation process is accompanied by temperature chaos, leading to dynamic pure state coexistence without violating the droplet scaling. Crucially, the interface geometry is not critical to these mechanisms, naturally incorporating the interface crossover from planar, fractal, to space-filling as the dimensionality increases, in line with the mean-field limit. Finally, the chaos picture provides profound insights into spin-glass dynamics such as aging, rejuvenation, and memory effect, while offering a streamlined reinterpretation of the complex metastate framework.
ER -